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                                                                    EXHIBIT 4.28

                       SUPPLEMENT TO WARRANT AGREEMENT

          THIS SUPPLEMENT TO WARRANT AGREEMENT, dated as of January 31, 2001
(the "Supplement"), by and among Transocean Sedco Forex Inc., a company
incorporated under the laws of the Cayman Islands ("Parent"), R&B Falcon
Corporation, a Delaware corporation (the "Company"), and American Stock Transfer
& Trust Company, a bank and trust company organized and existing under the laws
of New York (the "Warrant Agent").

                                  WITNESSETH:

          WHEREAS, pursuant to the Warrant Agreement dated as of April 22, 1999
(the "Warrant Agreement"), by and among the Company and the Warrant Agent, the
Company appointed the Warrant Agent to act as agent for the Company in
connection with the issuance, exchange, cancellation, replacement and exercise
of warrants (the "Warrants") to purchase 35 shares of common stock, par value
$.01 per share, of the Company ("Company Common Stock") issued pursuant to the
Warrant Agreement; and

          WHEREAS, pursuant to an Agreement and Plan of Merger, dated as of
August 19, 2000 (the "Merger Agreement"), by and among Parent, Transocean
Holdings Inc., a Delaware corporation and a wholly owned subsidiary of Parent
("Sub"), TSF Delaware Inc., a Delaware corporation and a wholly owned subsidiary
of Sub, and the Company (i) each outstanding share of Company Common Stock has
been converted into the right to receive .5 ordinary shares, par value $.01 per
share, of Parent ("Parent Ordinary Shares") and (ii) the Company has become an
indirect wholly owned subsidiary of Parent; and

          WHEREAS, pursuant to Section 4.2(f) of the Merger Agreement, Parent
has assumed the Warrants.

          NOW, THEREFORE, in consideration of the premises and the mutual
agreements herein set forth, the parties hereto agree as follows:

          1.   Parent hereby assumes all obligations of the Company under the
     Warrant Agreement and agrees to be bound by all of the provisions thereof,
     as amended by this Supplement.

          2.   In accordance with Section 17(1) of the Warrant Agreement, each
     Warrant shall represent the right, subject to the provisions contained in
     the Warrant Agreement and in the certificate evidencing such Warrant, to
     purchase from the Company (and the Company shall issue and sell to such
     holder of the Warrant) 17.5 Parent Ordinary Shares (the "Warrant Shares")
     on exercise of such Warrant and payment of the exercise price of $19.00 per
     Warrant Share (the "Exercise Price").

          3.   The words "not more than 10,500,000 shares of Common Stock of the
     Company" in Section 5(b) of the Warrant Agreement shall be amended and
     replaced by and read as "not more than 5,250,000 Parent Ordinary Shares."
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          4.   To the extent that any provision hereof conflicts with any
     provision of the Warrant Agreement, the provision hereof shall control.
     Except as expressly supplemented and amended hereby, the terms and
     conditions of the Warrant Agreement shall remain in full force and effect.

          5.   Notwithstanding the date of execution hereof, this Supplement
     shall be deemed effective as of the Effective Time (as defined in the
     Merger Agreement).

          6.   This Supplement shall be governed by and construed in accordance
     with the laws of New York.

          7.   This Supplement may be executed in three counterparts and each of
     such counterparts shall for all purposes be deemed to be an original, and
     all such counterparts shall together constitute but one and the same
     instrument.

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          IN WITNESS WHEREOF, the parties hereto have caused this Supplement to
be duly executed, as of the day and year first above written.

                                        TRANSOCEAN SEDCO FOREX INC.


                                        By:  /s/ Robert L. Long
                                             -----------------------------------
                                              Name:  Robert L. Long
                                              Title: Executive Vice President
                                                     and Chief Financial Officer

                                        R&B FALCON CORPORATION



                                        By:  /s/ Paul B. Loyd, Jr.
                                             -----------------------------------
                                              Name:  Paul B. Loyd, Jr.
                                              Title: Chairman and Chief
                                                     Executive Officer

                                        AMERICAN STOCK TRANSFER & TRUST COMPANY



                                        By:  /s/ Herbert J. Lemmer
                                             -----------------------------------
                                              Name:  Herbert J. Lemmer
                                              Title: Vice President

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