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                                                                    EXHIBIT 4.13


         AGREEMENT OF RESIGNATION, APPOINTMENT AND ACCEPTANCE, dated as of
January 15, 2002 by and among R&B Falcon Corporation, a Delaware corporation
(the "Issuer"), JPMorgan Chase Bank (successor to Texas Commerce Bank National
Association), a banking corporation duly organized and existing under the laws
of the State of New York ("Prior Trustee"), and THE BANK OF NEW YORK, a banking
corporation duly organized and existing under the laws of the State of New York
("Successor Trustee").

                                    RECITALS:

         WHEREAS, the Issuer and Prior Trustee entered into a Trust Indenture
dated as of December 22, 1998 by and between the Issuer and the Prior Trustee
(the "Indenture");

         WHEREAS, the Issuer desires to appoint Successor Trustee as Trustee,
Paying Agent and Registrar to succeed Prior Trustee in such capacities under the
Indenture; and

         WHEREAS, Successor Trustee is willing to accept such appointment as
Successor Trustee, Paying Agent and Registrar under the Indenture;

         NOW, THEREFORE, the Issuer, Prior Trustee and Successor Trustee, for
and in consideration of the premises and other good and valuable consideration,
the receipt and sufficiency of which are hereby acknowledged, hereby consent and
agree as follows:

                                    ARTICLE I

                                THE PRIOR TRUSTEE

         SECTION 1.01 Prior Trustee hereby resigns as Trustee, Paying Agent and
Registrar under the Indenture with respect to all Securities (as defined in the
Indenture).

         SECTION 1.02 Prior Trustee hereby assigns, transfers, delivers and
confirms to Successor Trustee all right, title and interest of Prior Trustee in
and to the trusts of the Trustee under the Indenture and all the rights, powers
and trusts of the Trustee under the Indenture. Prior Trustee shall execute and
deliver such further instruments and shall do such other things as Successor
Trustee may reasonably require so as to more fully and certainly vest and
confirm in Successor Trustee all the rights, powers and trust hereby assigned,
transferred, delivered and confirmed to Successor Trustee as Trustee, Paying
Agent and Registrar.



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                                   ARTICLE II

                                   THE ISSUER

         SECTION 2.01 The Issuer hereby accepts the resignation of Prior Trustee
as Trustee, Paying Agent and Registrar under the Indenture with respect to all
Securities.

         SECTION 2.02 All conditions relating to the appointment of The Bank of
New York as Successor Trustee, Paying Agent and Registrar under the Indenture
have been met by the Issuer, and the Issuer hereby appoints Successor Trustee as
Trustee, Paying Agent and Registrar under the Indenture with respect to all
Securities with like effect as if originally named as Trustee, Paying Agent and
Registrar in the Indenture.

                                   ARTICLE III

                              THE SUCCESSOR TRUSTEE

         SECTION 3.01 Successor Trustee hereby represents and warrants to Prior
Trustee and to the Issuer that Successor Trustee is not disqualified to act as
Trustee under the Indenture.

         SECTION 3.02 Successor Trustee hereby accepts its appointment as
Successor Trustee, Paying Agent and Registrar under the Indenture with respect
to all Securities and accepts the rights, powers, duties and obligations of
Prior Trustee as Trustee, Paying Agent and Registrar under the Indenture, upon
the terms and conditions set forth therein, with like effect as if originally
named as Trustee, Paying Agent and Registrar under the Indenture.

                                   ARTICLE IV

                                  MISCELLANEOUS

         SECTION 4.01 This Agreement and the resignation, appointment and
acceptance effected hereby shall be effective as of the date hereof.

         SECTION 4.02 This Agreement shall be governed by and construed in
accordance with the laws of State of New York, but without giving effect to
applicable principles of conflicts of law to the extent the application of the
laws of another jurisdiction would be required thereby.

         SECTION 4.03 This Agreement may be executed in any number of
counterparts each of which shall be an original, but such counterparts shall
together constitute but one and the same instrument.



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         IN WITNESS WHEREOF, the parties hereto have caused this Agreement of
Resignation Appointment and Acceptance to be duly executed and acknowledged all
as of the day and year first above written.


                                                R&B FALCON CORPORATION


                                                By:    /s/ GREGORY L. CAUTHEN
                                                    ----------------------------
                                                    Name:  Gregory L. Cauthen
                                                          ----------------------
                                                    Title: Vice President and
                                                           Treasurer
                                                           ---------------------


                                                JPMORGAN CHASE BANK

                                                AS PRIOR TRUSTEE


                                                By:    /s/ MAURI J. COWEN
                                                    ----------------------------
                                                    Name:  Mauri J. Cowen
                                                          ----------------------
                                                    Title: Vice President and
                                                           Trust Officer
                                                           ---------------------


                                                THE BANK OF NEW YORK

                                                AS SUCCESSOR TRUSTEE

                                                By:    /s/ REMO J. REALE
                                                    ----------------------------
                                                    Name:  Remo J. Reale
                                                          ----------------------
                                                    Title: Vice President
                                                           ---------------------



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