EXHIBIT 4.6

     FIRST  SUPPLEMENTAL  INDENTURE (this "First  Supplemental  Indenture")
dated  as  of December 23, 1997, among R&B Falcon Corporation,  a  Delaware
corporation ("Parent"), Reading & Bates Corporation, a Delaware corporation
(the  "Company"), and IBJ Schroder Bank & Trust Company, a New York banking
corporation,   as  trustee  (the  "Trustee"),  under  the  Indenture   (the
"Indenture")  dated  as of August 29, 1989, between  the  Company  and  the
Trustee.

          WHEREAS pursuant to an Agreement and Plan of Merger dated  as  of
July  10,  1997  (the  "Merger Agreement"), among Parent,  FDC  Acquisition
Corp.,  a  Delaware  corporation and a wholly owned  subsidiary  of  Parent
("SubF"), Reading & Bates Acquisition Corp., a Delaware corporation  and  a
wholly  owned subsidiary of Parent ("SubR"), Falcon Drilling Company,  Inc.
("FDC")  and the Company, SubF merged with and into FDC (the "FDC Merger"),
SubR merged with and into the Company (the "R&B Merger", and, together with
the  FDC Merger, the "Mergers") with FDC and the Company continuing as  the
surviving corporations in the Mergers, and thereupon becoming wholly  owned
subsidiaries of Parent; and

          WHEREAS pursuant to the Merger Agreement, each outstanding  share
of  common  stock, par value $0.05 per share, of the Company  ("R&B  Common
Stock") will be converted into 1.18 shares of common stock, par value  $.01
per share, of Parent ("Parent Common Stock"); and

          WHEREAS  as  a result of the conversion of R&B Common Stock  into
Parent  Common  Stock, Parent is required to execute  and  deliver  to  the
Trustee  a  supplemental  indenture  pursuant  to  Section  12.05  of   the
Indenture;

          NOW  THEREFORE,  Parent  hereby covenants  and  agrees  with  the
Trustee for the benefit of the present and future holders of the Securities
as follows:

                                 ARTICLE I

          SECTION  1.01   Conversion Right.  The holder  of  each  Security
outstanding  as  of  the date the Mergers are consummated  shall  have  the
right, during the period such Security shall be convertible as specified in
Section  12.01  of the Indenture, to convert such Security into  shares  of
Parent  Common Stock equal to 1.18 times the number of shares of R&B Common
Stock  such  holder  would  have had the right to receive  upon  conversion
immediately prior to the date of the consummation of the Mergers.

          SECTION 1.02  Antidilution Adjustments.  The conversion price  in
effect  at any time shall be subject to adjustment as set forth in  Section
12.04 of the Indenture.

                                ARTICLE II

          SECTION  2.01   Amendment to Definition of "Common  Stock".   The
definition of "Common Stock" set forth in Section 1.01 of the Indenture  is
hereby  amended by deleting the proviso thereto and replacing it  with  the
following:

          "provided,  however,  that for the purposes  of  Sections  12.02,
          12.03,  12.04,  12.05,  12.06, 12.07,  12.08,  12.09  and  12.11,
          "Common  Stock"  means  only shares of the  class  designated  as
          Common Stock of the Parent as of December 23, 1997 or as the same
          may  be  reconstituted from time to time and stock of  any  other
          class into which such shares may hereafter have been changed.  As
          of December 23, 1997, the Common Stock, par value $.01 per share,
          of  the Parent constitutes the Common Stock of the Parent for the
          purposes  of  Sections 12.02, 12.03, 12.04, 12.05, 12.06,  12.07,
          12.08, 12.09 and 12.11 herein."


          SECTION  2.02  Definition of "Parent".  The following  definition
shall be added to Section 1.01 of the Indenture:

          "Parent:

               The  term  "Parent"  shall mean R&B  FALCON  CORPORATION,  a
corporation organized under the laws of the State of Delaware."

          SECTION  2.03   Amendment to Section 12.  Sections 12.04,  12.05,
12.06,  12.07,  12.09, 12.11 and 12.14 of the Indenture are hereby  amended
such  that each reference therein to "the Company" shall be deemed to  read
"the Parent".

                                ARTICLE III

          SECTION  3.01  First Supplemental Indenture.  The Trustee accepts
the  provisions  of this First Supplemental Indenture upon  the  terms  and
conditions set forth in the Indenture as amended by this First Supplemental
Indenture.

          SECTION 3.02  Other Terms of Indenture.  Except insofar as herein
otherwise  expressly provided, all the provisions, terms and conditions  of
the  Indenture are in all respects ratified and confirmed and shall  remain
in full force and effect.

          SECTION 3.03  Definitions.  Capitalized terms used herein and not
defined  herein have the meanings ascribed to such terms in  the  Indenture
unless the context of this First Supplemental Indenture otherwise requires.

          SECTION  3.04  Governing Law.  This First Supplemental  Indenture
shall  be deemed to have been made under the laws of the State of New  York
and  shall  for  all purposes be governed by, and construed  in  accordance
with, the laws of such State.

          SECTION  3.05   Counterparts.  This First Supplemental  Indenture
may  be  executed  in any number of counterparts, each of  which  shall  be
deemed  to  be  an  original, but all of which when  taken  together  shall
constitute but one instrument.
          SECTION  3.06  Effective Time.  This First Supplemental Indenture
shall  become effective at 11:59 p.m. (Eastern Standard Time)  on  December
31, 1997.

          SECTION  3.07   Separability.  In case any one  or  more  of  the
provisions  contained in this First Supplemental Indenture  shall  for  any
reason be held to be invalid, illegal or unenforceable in any respect, such
invalidity,  illegality  or unenforceability shall  not  affect  any  other
provision  of  this  First Supplemental Indenture,  the  Indenture  or  the
Securities,  but this First Supplemental Indenture, the Indenture  and  the
Securities  shall be construed as if such invalid, illegal or unenforceable
provision had never been contained herein or therein.

          IN  WITNESS  WHEREOF, the parties hereto have caused  this  First
Supplemental  Indenture to be duly executed by their respective  authorized
officers as of the date first written above.

                              R&B FALCON CORPORATION,

                              by
                                 ________________________
                                 Name:  Steven A. Webster
                                 Title: Chief Executive Officer

                              Attest:

                                 ________________________
                                 Name:

                                 READING & BATES CORPORATION,

                                 by

                                 ________________________
                                 Name:  Paul B. Loyd, Jr.
                                 Title: Chairman of the Board
                                        and Chief Executive Officer

                                 Attest:

                                 ________________________
                                 Name:

                                 IBJ SCHRODER BANK & TRUST COMPANY
                                 as Trustee,

                                 by

                                 ________________________
                                 Name:  Luis Perez
                                 Title: Assistant Vice President

                                 Attest:

                                 ________________________
                                 Name: