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                                                                    EXHIBIT 4.15



                             R&B Falcon Corporation



                                    as Issuer



                                   $87,112,000

                          9.125% Senior Notes due 2003

                                  $300,000,000

                           9.50% Senior Notes due 2008



                          First Supplemental Indenture



                          Dated as of ______ ____, 2002

                   To Indenture dated as of December 22, 1998



                              The Bank of New York

                                   as Trustee




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                  FIRST SUPPLEMENTAL INDENTURE, dated as of January ___, 2002
(this "Supplemental Indenture"), between R&B Falcon Corporation, a Delaware
corporation (the "Issuer"), and The Bank of New York, as trustee (the
"Trustee").

                  WITNESSETH:

                  WHEREAS, the Issuer and The Chase Manhattan Bank, National
Association, as a predecessor to the Trustee, executed and delivered an
Indenture, dated as of December 22, 1998 (the "Indenture"), providing for the
issuance of $87,112,000 principal amount of 9.125% Notes due 2003 and
$300,000,000 principal amount of 9.50% Notes due 2008; all capitalized terms
used herein and not defined are used herein as defined in the Indenture;

                  WHEREAS, pursuant to Section 8.02 of the Indenture, the Issuer
and the Trustee may amend or supplement the Indenture with respect to the
Securities of any series with the written consent of the Holders of a majority
in aggregate principal amount of the outstanding Securities of such series;

                  WHEREAS, Transocean Sedco Forex Inc., a Cayman Islands company
("Transocean Sedco Forex"), has offered to exchange all of the outstanding
Securities of each series, upon the terms and subject to the conditions set
forth in its Prospectus and Consent Solicitation Statement, dated January 31,
2002, and in the related Letter of Transmittal and Consent (each such offer, an
"Exchange Offer"); in connection therewith Transocean Sedco Forex has been
soliciting written consents of the Holders to the amendments to the Indenture
set forth herein (and to the execution of this Supplemental Indenture), and
Transocean Sedco Forex has now obtained such written consents from the Holders
of a majority in aggregate principal amount of the outstanding Securities of
each series; accordingly, this Supplemental Indenture and the amendments set
forth herein are authorized pursuant to Section 8.02 of the Indenture referred
to above;

                  WHEREAS, the execution and delivery of this Supplemental
Indenture has been duly authorized by the parties hereto, and all other acts
necessary to make this Supplemental Indenture a valid and binding supplement to
the Indenture effectively amending the Indenture as set forth herein have been
duly taken;

                  NOW, THEREFORE, THIS INDENTURE WITNESSETH, that, for and in
consideration of the above premises, it is mutually covenanted and agreed, for
the equal and proportionate benefit of all Holders of the Securities, as
follows:

                  Section 1. Amendments to the Indenture.

                  Upon consummation of the exchange by Transocean Sedco Forex of
all Securities of a series validly tendered pursuant to the applicable Exchange
Offer and not withdrawn prior to the expiration date for such Exchange Offer (as
notified to the Trustee by Transocean Sedco Forex, upon which notification the
Trustee may rely), then automatically (without further act by any person) with
respect to all outstanding Securities of such series: (a) Sections 3.03, 3.05,
3.06, 3.07, 3.09, 3.10, 3.11, 3.12, 3.13, 4.01 and 4.02 of the Indenture shall
be deleted and the Issuer shall be released from its obligations thereunder, (b)
any failure by the Issuer to comply with the terms of any of the foregoing
Sections of the Indenture (whether before or after the execution of this
Supplemental Indenture) shall no longer constitute a default or an Event of
Default under the Indenture and shall no longer have any other consequence under
the Indenture and (c) Clauses (4), (5), (6) and (7) of Section 5.01 of the
Indenture shall be deleted and the events described therein no longer constitute
Events of Default under the Indenture. In conjunction with the amendments
identified in the immediately preceding sentence, the following defined terms
used in the Indenture shall be deleted: "Attributable Indebtedness";
"Consolidated EBITDA Coverage Ratio"; "Consolidated Net Income"; "Consolidated
Net Worth"; "Hedging Obligations"; "Incurrence"; "Indebtedness"; "Restricted
Subsidiary"; "Sale/Leaseback Transactions"; and "Suspended Covenants".

                  Section 2. Ratification.

                  Except as hereby expressly amended, the Indenture is in all
respects ratified and confirmed and all the terms, provisions and conditions
thereof shall be and remain in full force and effect.


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                  Section 3. Governing Law.

                  THIS SUPPLEMENTAL INDENTURE, THE INDENTURE AS SUPPLEMENTED AND
AMENDED HEREBY AND THE SECURITIES SHALL BE GOVERNED BY, AND CONSTRUED IN
ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

                  Section 4. Counterpart Originals.

                  The parties may sign any number of copies of this Supplemental
Indenture. Each signed copy shall be an original, but all of them together
represent the same agreement. One signed copy is enough to prove this
Supplemental Indenture.

                  Section 5. The Trustee.

                  The recitals in this Supplemental Indenture shall be taken as
the statements of the Issuer and the Trustee assumes no responsibility for their
correctness. The Trustee shall be responsible or accountable in any manner
whatsoever for or with respect to the validly or sufficiency of this
Supplemental Indenture.

                  IN WITNESS WHEREOF, the parties hereto have caused this
Supplemental Indenture to be duly executed as of the date first written above.



                                               R&B Falcon Corporation
                                               By:
                                                  ------------------------------
                                                  Name:
                                                  Title:

                                               The Bank of New York, as Trustee
                                               By:
                                                  ------------------------------
                                                  Name:
                                                  Title: