UNITED STATES
                     SECURITIES AND EXCHANGE COMMISSION
                              Washington, D.C.

                                SCHEDULE 13G

                 UNDER THE SECURITIES EXCHANGE ACT OF 1934
                             (AMENDMENT NO. 1)(1)

                      UNITED STATES STEEL CORPORATION
---------------------------------------------------------------------------
                              (Name of Issuer)

                                COMMON STOCK
---------------------------------------------------------------------------
                       (Title of Class of Securities)

                                 912909108
               ----------------------------------------------
                               (CUSIP Number)

                             DECEMBER 31, 2003
               ----------------------------------------------
        (Date of Event Which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this
Schedule is filed:

     |_|   Rule 13d-1(b)
     |X|   Rule 13d-1(c)
     |_|   Rule 13d-1(d)

(1) The remainder of this cover page shall be filled out for a reporting
person's initial filing on this form with respect to the subject class of
securities, and for any subsequent amendment containing information which
would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities
Exchange Act of 1934, as amended (the "Act") or otherwise subject to the
liabilities of that section of the Act but shall be subject to all other
provisions of the Act (however, see the Notes).



                                SCHEDULE 13G


CUSIP NO.        912909108                      PAGE      2    OF   11   PAGES

  1     NAME OF REPORTING PERSON
        I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

            APPALOOSA INVESTMENT LIMITED PARTNERSHIP I

  2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*          (a)      |_|
                                                                   (b)      |_|

  3     SEC USE ONLY


  4     CITIZENSHIP OR PLACE OF ORGANIZATION

            DELAWARE


                   5    SOLE VOTING POWER
   NUMBER OF
                            -0-
     SHARES
                   6    SHARED VOTING POWER
  BENEFICIALLY
                            3,304,601
    OWNED BY

      EACH         7    SOLE DISPOSITIVE POWER

   REPORTING
                            -0-
     PERSON
                   8    SHARED DISPOSITIVE POWER
      WITH
                            3,304,601

  9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

            3,304,601

  10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
                                                                            |_|

  11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

            3.2%

  12    TYPE OF REPORTING PERSON*
            PN




                                SCHEDULE 13G


CUSIP NO.        912909108                      PAGE      3    OF   11   PAGES

  1     NAME OF REPORTING PERSON
        I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

            PALOMINO FUND LTD.

  2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*          (a)      |_|
                                                                   (b)      |_|

  3     SEC USE ONLY


  4     CITIZENSHIP OR PLACE OF ORGANIZATION

            BRITISH VIRGIN ISLANDS


                   5    SOLE VOTING POWER

   NUMBER OF
                            -0-
     SHARES
                   6    SHARED VOTING POWER
  BENEFICIALLY
                            2,995,399
    OWNED BY

      EACH         7    SOLE DISPOSITIVE POWER

   REPORTING
                            -0-
     PERSON
                   8    SHARED DISPOSITIVE POWER
      WITH
                            2,995,399

  9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

            2,995,399

  10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
                                                                            |_|

  11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

            2.8%

  12    TYPE OF REPORTING PERSON*
            CO




                                SCHEDULE 13G


CUSIP NO.        912909108                      PAGE      4    OF   11   PAGES

  1     NAME OF REPORTING PERSON
        I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

            APPALOOSA MANAGEMENT L.P.

  2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*          (a)      |_|
                                                                   (b)      |_|

  3     SEC USE ONLY


  4     CITIZENSHIP OR PLACE OF ORGANIZATION

            DELAWARE


                   5    SOLE VOTING POWER

   NUMBER OF
                            -0-
     SHARES
                   6    SHARED VOTING POWER
  BENEFICIALLY
                            6,200,000
    OWNED BY

      EACH         7    SOLE DISPOSITIVE POWER

   REPORTING
                            -0-
     PERSON
                   8    SHARED DISPOSITIVE POWER
      WITH
                            6,200,000

  9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

            6,200,000

  10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
                                                                            |_|

  11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

            6.0%

  12    TYPE OF REPORTING PERSON*
            PN




                                SCHEDULE 13G


CUSIP NO.        912909108                      PAGE      5    OF   11   PAGES

  1     NAME OF REPORTING PERSON
        I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

            APPALOOSA PARTNERS INC.

  2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*          (a)      |_|
                                                                   (b)      |_|

  3     SEC USE ONLY


  4     CITIZENSHIP OR PLACE OF ORGANIZATION

            DELAWARE


                   5    SOLE VOTING POWER

   NUMBER OF
                            -0-
     SHARES
                   6    SHARED VOTING POWER
  BENEFICIALLY
                            6,200,000
    OWNED BY

      EACH         7    SOLE DISPOSITIVE POWER

   REPORTING
                            -0-
     PERSON
                   8    SHARED DISPOSITIVE POWER
      WITH
                            6,200,000

  9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

            6,200,000

  10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
                                                                            |_|

  11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

            6.0%

  12    TYPE OF REPORTING PERSON*
            CO




                                SCHEDULE 13G


CUSIP NO.        912909108                      PAGE      6    OF   11   PAGES

  1     NAME OF REPORTING PERSON
        I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

            DAVID A. TEPPER

  2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*          (a)      |_|
                                                                   (b)      |_|

  3     SEC USE ONLY


  4     CITIZENSHIP OR PLACE OF ORGANIZATION

            UNITED STATES

                   5    SOLE VOTING POWER

   NUMBER OF
                            -0-
     SHARES
                   6    SHARED VOTING POWER
  BENEFICIALLY
                            6,200,000
    OWNED BY

      EACH         7    SOLE DISPOSITIVE POWER

   REPORTING
                            -0-
     PERSON
                   8    SHARED DISPOSITIVE POWER
      WITH
                            6,200,000

  9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

            6,200,000

  10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*
                                                                            |_|

  11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

            6.0%

  12    TYPE OF REPORTING PERSON*
            IN




Item 1.

     (a)  NAME OF ISSUER:

          United States Steel Corporation

     (b)  ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

          660 Grant Street, Room 1500
          Pittsburgh, PA  15219-2800

Item 2.

     (a)  NAME OF PERSON FILING:

          This Statement is being filed by and on behalf of Appaloosa
          Investment Limited Partnership I ("AILP"), Palomino Fund Ltd.
          ("Palomino"), Appaloosa Management L.P. ("AMLP"), Appaloosa
          Partners Inc. ("API") and David A. Tepper ("Mr. Tepper" and,
          together with AILP, Palomino, AMLP and API, the "Reporting
          Persons"). Mr. Tepper is the sole stockholder and the President
          of API. API is the general partner of, and Mr. Tepper owns a
          majority of the limited partnership interests in, AMLP. AMLP is
          the general partner of AILP and acts as investment adviser to
          Palomino.

     (b)  ADDRESS OF PRINCIPAL BUSINESS OFFICE:

          The business address of each of the Reporting Persons is c/o
          Appaloosa Management L.P., 26 Main Street, Chatham, NJ 07928.

     (c)  CITIZENSHIP:

          AILP is a Delaware limited partnership. Palomino is a British
          Virgin Islands corporation. AMLP is a Delaware limited
          partnership. API is a Delaware corporation. Mr. Tepper is a
          citizen of the United States.

     (d)  TITLE OF CLASS OF SECURITIES:

          Common Stock, par value $1.00 per share.

     (e)  CUSIP NUMBER:  912909108

Item 3.     IF THIS STATEMENT IS FILED PURSUANT TO RULES 13d-1(b), OR
            13-2(b), CHECK WHETHER THE PERSON FILING IS A:

     (a) [  ] Broker or Dealer registered under Section 15 of the Act
              (15 U.S.C. 78o);

     (b) [  ] Bank as defined in Section 3(a)(6) of the Act (15 U.S.C. 78c);

     (c) [  ] Insurance Company as defined in Section 3(a)(19) of the Act
              (15 U.S.C. 78c);

     (d) [  ] Investment Company registered under Section 8 of the Investment
              Company Act (15 U.S.C. 80a-8);

     (e) [  ] An investment advisor in accordance with Section
              240.13d-1(b)(1)(ii)(E);

     (f) [  ] An employee benefit plan or endowment fund in accordance
              with Section 240.13d-1(b)(1)(ii)(F);

     (g) [  ] A parent holding company or control person, in accordance
              with Section 240.13d-1(b)(1)(ii)(G);

     (h) [  ] A savings association as defined in Section 3(b) of the
              Federal Deposit Insurance Act (12 U.S.C. 1813);

     (i) [  ] A church plan that is excluded from the definition of an
              investment company under Section 3(c)(14) of the Investment
              Company Act of 1940 (15 U.S.C. 80a-3);

     (j) [  ] Group, in accordance with Section 240.13d-1(b)(1)(ii)(H)

If this statement is filed pursuant to ss. 240.13d-1(c), check this box. |X|

Item 4.   OWNERSHIP:

          The percentages set forth in this Item 4 are based on there being
          103,277,374 shares of Common Stock outstanding as of October 31,
          2003 as disclosed in United States Steel Corporation's Form 10-Q
          filed on November 7, 2003 for the quarterly period ended
          September 30, 2003.

AILP
----

(a)  AMOUNT BENEFICIALLY OWNED:  3,304,601

(b)  PERCENT OF CLASS:  3.2%

(c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

     (i)   sole power to vote or to direct the vote: -0-

     (ii)  shared power to vote or to direct the vote: 3,304,601

     (iii) sole power to dispose or to direct the disposition of: -0-

     (iv)  shared power to dispose or to direct the disposition of: 3,304,601

Palomino
--------

(a)  AMOUNT BENEFICIALLY OWNED:  2,895,399

(b)  PERCENT OF CLASS:  2.8%

(c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

     (i)   sole power to vote or to direct the vote: -0-

     (ii)  shared power to vote or to direct the vote: 2,895,399

     (iii) sole power to dispose or to direct the disposition of: -0-

     (iv)  shared power to dispose or to direct the disposition of: 2,895,399

AMLP
----

(a)  AMOUNT BENEFICIALLY OWNED:  6,200,000

(b)  PERCENT OF CLASS:  6.0%

(c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

     (i)   sole power to vote or to direct the vote: -0-

     (ii)  shared power to vote or to direct the vote: 6,200,000

     (iii) sole power to dispose or to direct the disposition of: -0-

     (iv)  shared power to dispose or to direct the disposition of: 6,200,000

API
---

(a)  AMOUNT BENEFICIALLY OWNED:  6,200,000

(b)  PERCENT OF CLASS:  6.0%

(c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

     (i)   sole power to vote or to direct the vote: -0-

     (ii)  shared power to vote or to direct the vote: 6,200,000

     (iii) sole power to dispose or to direct the disposition of: -0-

     (iv)  shared power to dispose or to direct the disposition of: 6,200,000

David A. Tepper
---------------

(a)  AMOUNT BENEFICIALLY OWNED:  6,200,000

(b)  PERCENT OF CLASS:  6.0%

(c)  NUMBER OF SHARES AS TO WHICH SUCH PERSON HAS:

     (i)   sole power to vote or to direct the vote: -0-

     (ii)  shared power to vote or to direct the vote: 6,200,000

     (iii) sole power to dispose or to direct the disposition of: -0-

     (iv)  shared power to dispose or to direct the disposition of: 6,200,000

Item 5.   OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS:

          If this statement is being filed to report the fact that as of
the date hereof the reporting person has ceased to be the beneficial owner
of more than five percent of the class of securities, check the following:
|_|

Item 6.   OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER
          PERSON:

          Not applicable.

Item 7.   IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH
          ACQUIRED THE SECURITY BEING REPORTED ON BY THE PARENT
          HOLDING COMPANY:

          Not applicable.

Item 8.   IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP:

          Not applicable.

Item 9.   NOTICES OF DISSOLUTION OF GROUP:

          Not applicable.

Item 10.  CERTIFICATION:

          By signing below I certify that, to the best of my knowledge and
          belief, the securities referred to above were not acquired and
          are not held for the purpose of or with the effect of changing or
          influencing the control of the issuer of the securities and were
          not acquired and are not held in connection with or as a
          participant in any transaction having that purpose or effect.



                             SIGNATURE PAGE
                             --------------

          After reasonable inquiry and to the best of my knowledge and
belief, I certify that the information set forth in this statement is true,
complete and correct.

Dated:  January 5, 2004

                                APPALOOSA INVESTMENT LIMITED
                                PARTNERSHIP I

                                By:  APPALOOSA MANAGEMENT L.P.,
                                     Its General Partner

                                     By:  APPALOOSA PARTNERS INC.,
                                          Its General Partner

                                          By:  /s/ David A. Tepper
                                              --------------------------------
                                              Name:  David A. Tepper
                                              Title: President


                                PALOMINO FUND LTD.

                                By:  APPALOOSA MANAGEMENT L.P.,
                                     Its Investment Adviser

                                     By:  APPALOOSA PARTNERS INC.,
                                          Its General Partner

                                          By:  /s/ David A. Tepper
                                              --------------------------------
                                              Name:  David A. Tepper
                                              Title: President


                                APPALOOSA MANAGEMENT L.P.

                                By:  APPALOOSA PARTNERS INC.,
                                     Its General Partner

                                     By:  /s/ David A. Tepper
                                         -------------------------------------
                                         Name:  David A. Tepper
                                         Title: President


                                APPALOOSA PARTNERS INC.

                                By:  /s/ David A. Tepper
                                    ------------------------------------------
                                    Name:  David A. Tepper
                                    Title: President

                                /s/ David A. Tepper
                                ----------------------------------------------
                                David A. Tepper



                                EXHIBIT A
                                ---------

                         JOINT FILING AGREEMENT
                         ----------------------

The undersigned agree that the foregoing Statement on Schedule 13G
(including any and all amendments thereto) is being filed with the
Securities and Exchange Commission on behalf of each of the undersigned
pursuant to Rule 13d-1(k) under the Act and further agree that this Joint
Filing Agreement be included as an Exhibit to such joint filings.

Dated:  January 5, 2004

                                APPALOOSA INVESTMENT LIMITED
                                PARTNERSHIP I

                                By:  APPALOOSA MANAGEMENT L.P.,
                                     Its General Partner

                                     By:  APPALOOSA PARTNERS INC.,
                                          Its General Partner

                                          By:  /s/ David A. Tepper
                                              --------------------------------
                                              Name:  David A. Tepper
                                              Title: President


                                PALOMINO FUND LTD.

                                By:  APPALOOSA MANAGEMENT L.P.,
                                     Its Investment Adviser

                                     By:  APPALOOSA PARTNERS INC.,
                                          Its General Partner

                                          By:  /s/ David A. Tepper
                                              --------------------------------
                                              Name:  David A. Tepper
                                              Title: President


                                APPALOOSA MANAGEMENT L.P.

                                By:  APPALOOSA PARTNERS INC.,
                                     Its General Partner

                                     By:  /s/ David A. Tepper
                                         -------------------------------------
                                         Name:  David A. Tepper
                                         Title: President


                                APPALOOSA PARTNERS INC.

                                By:  /s/ David A. Tepper
                                    ------------------------------------------
                                    Name:  David A. Tepper
                                    Title: President

                                /s/ David A. Tepper
                                ----------------------------------------------
                                David A. Tepper