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                                                                    EXHIBIT 4.30

              SUPPLEMENT TO WARRANT REGISTRATION RIGHTS AGREEMENT

          THIS SUPPLEMENT TO WARRANT REGISTRATION RIGHTS AGREEMENT, dated as of
January 31, 2001 (the "Supplement"), is executed by Transocean Sedco Forex Inc.,
a company incorporated under the laws of the Cayman Islands ("Parent"), and R&B
Falcon Corporation, a Delaware corporation (the "Company").

                                  WITNESSETH:

          WHEREAS, pursuant to the Warrant Registration Rights Agreement, dated
as of April 22, 1999 (the "Registration Rights Agreement"), by and between the
Company and Donaldson, Lufkin & Jenrette Securities Corporation, the Company
agreed to provide the registration rights set forth therein; and

          WHEREAS, pursuant to the Warrant Agreement dated as of April 22, 1999
(the "Warrant Agreement"), by and among 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"), 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, $.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 and the
Supplement to Warrant Agreement dated as of January 31, 2001, by and among the
Company, Parent and the Warrant Agent, Parent has assumed the Warrants; and

          WHEREAS, a registration statement on Form S-4 (Registration No.
333-46374) (the "Registration Statement") covering the issuance of the Warrants
pursuant to the Merger and the issuance of the Parent Ordinary Shares upon
exercise of the Warrants (the "Warrant Shares") has been declared effective by
the Securities and Exchange Commission, and Warrants and Warrant Shares issued
pursuant thereto will be freely transferable, except for restrictions applicable
to "affiliates" of the Company under the Securities Act of 1933, as amended.

          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
     Registration Rights Agreement and agrees to be bound by all of the
     provisions thereof, as amended by this Supplement (it being understood
     that, provided the Registration Statement remains effective until the
     earlier of the expiration or

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     exercise of all Warrants, there will be no Transfer Restricted Securities
     (as defined in the Registration Rights Agreement)).

          2.   To the extent that any provision hereof conflicts with any
     provision of the Registration Rights Agreement, the provision hereof shall
     control. Except as expressly amended hereby, the terms and conditions of
     the Registration Rights Agreement shall remain in full force and effect.

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

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

          5.   This Supplement may be executed in two 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.

                                       2
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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