EXHIBIT 10.4

                     TERMINATION AGREEMENT


This  Termination Agreement (the "Agreement"), entered  into  and
effective as of July 31, 1999 (the "Effective Date"), is  between
Douglas  E.  Swanson  ("Swanson")  and  Cliffs  Drilling  Company
("CDC").

In  consideration of the mutual obligations set out below and  in
that agreement of the same effective date between Swanson and CDC
and substantially in the form attached as Exhibit "A" hereto (the
"Non-Compete Agreement"), the parties agree as follows:

     1.   As   of   the   Effective  Date  Swanson  tenders   his
          resignation  as President, Chief Executive Officer  and
          Director  of  CDC  and  as a director,  officer  and/or
          employee  of  all direct and indirect subsidiaries  and
          affiliated  companies  of CDC [other  than  R&B  Falcon
          Corporation ("RBF") of which Swanson shall continue  to
          be  a  director], as the case may be, which CDC accepts
          on  its  behalf and on behalf of RBF, such subsidiaries
          and affiliated companies.

     2.   Upon  execution  of this Agreement and subject  to  the
          payment and other obligations of CDC and RBF set out in
          this  Agreement and in the Non-Compete Agreement,  this
          Agreement and the Non-Compete Agreement constitute full
          satisfaction  of  all  obligations  of  CDC  under  and
          pursuant  to  Section  4 of that  Employment  Agreement
          dated  as of December 1, 1998 between Swanson  and  CDC
          (the "Employment Agreement").

     3.   Notwithstanding anything to the contrary  in  (i)  this
          Agreement,  (ii) Section 7 of the Employment Agreement,
          or  (iii) the Non-Compete Agreement, Swanson shall  not
          be  entitled  to, and CDC shall have no  obligation  to
          make  to  Swanson, any Gross-Up Payment (as defined  in
          Section 7 of the Employment Agreement) with respect  to
          any  Excise  Tax  (as  defined  in  Section  7  of  the
          Employment Agreement) imposed on or with respect to the
          stock  options held by Swanson under the  Stock  Option
          Agreements, which are referred to in  Section 4 of  the
          Non-Compete Agreement, provided, however, the remaining
          obligations  of  CDC  in Section 7  of  the  Employment
          Agreement  shall  continue to  be  in  full  force  and
          effect.

     4.   Swanson  shall have the option, exercisable if  at  all
          only  by  written notice to CDC given  within  60  days
          following the Effective Date, to acquire full ownership
          of those certain split dollar insurance policies, being
          Policy  No.  13905796 dated January 1, 1997 and  Policy
          No.  13347465 dated January 1, 1995, each issued by The
          Northwestern  Mutual Life Insurance  Company,  together
          with a release of the collateral assignments granted in
          favor of CDC under and pursuant to the two Split Dollar
          Insurance  Agreements  dated January  1,  1995  between
          Swanson  and  CDC  (the "Insurance  Agreements"),  upon
          payment by Swanson of the Company's Policy Interest (as
          defined  in the Insurance Agreements).  If such  option
          is  exercised and upon  payment of the sum referred  in
          the  preceding sentence by Swanson and release  of  the
          collateral assignments by CDC, neither Swanson nor  the
          Company  shall  thereafter have any obligation  to  the
          other under the Insurance Agreements.

          For  purposes of this Section 4, such notice, if given,
          shall  be  addressed as follows and sent via registered
          or certified mail:

               Cliffs Drilling Company
               901 Threadneedle, Suite 200
               Houston, Texas 77079

               Attention:  Mr. Paul B. Loyd, Jr.

     5.   The Agreement shall be binding upon and shall inure  to
          the   benefit   of   the  parties,   their   respective
          representatives,  agents,  attorneys,  successors   and
          assigns,  and,  in  particular,  without  limiting  the
          generality   of  the  foregoing,  to  CDC's  directors,
          officers   and   employees  and  to  Swanson's   heirs,
          executors,    administrators,   legal   and    personal
          representatives and assigns.

     6.   This  Agreement shall be deemed to be a  contract  made
          under  and governed by, the laws of the State of Texas,
          without reference to principles of conflicts of law.

     7.   This    Agreement   and   the   Non-Compete   Agreement
          constitutes  the complete and entire agreement  between
          the  parties.   Subject to Sections  4,  5  and  7  (as
          modified  by  Section  3  of  this  Agreement)  of  the
          Employment  Agreement,  this Agreement  supersedes  and
          cancels  all  prior or contemporaneous representations,
          promises  or  agreements  between  the  parties.   This
          Agreement  cannot  be  amended or  modified  except  by
          written agreement signed by each of the parties hereto.

     8.   The  provisions of this Agreement are severable.  If  a
          court or other tribunal of competent jurisdiction rules
          any   provision  of  this  Agreement  is   invalid   or
          unenforceable, such ruling will not affect the validity
          or   enforceability  of  any  other  provision  of  the
          Agreement,  and this Agreement shall be  deemed  to  be
          modified  and  amended so as to be enforceable  to  the
          extent permitted by law.


This Agreement is signed in Houston, Texas on July     , 1999.



                              ________________________
                              Douglas E. Swanson



                              CLIFFS DRILLING COMPANY



                              By:_____________________
                                 Its duly authorized
                                 officer


                                             EXHIBIT "A"


                           AGREEMENT


This  Agreement (the "Agreement"), entered into and effective  as
of  July  31,  1999 (the "Effective Date"), is among  Douglas  E.
Swanson  ("Swanson"),  Cliffs Drilling Company  ("CDC")  and  R&B
Falcon Corporation ("RBF").

In  consideration  of  the  mutual  obligations  set  out  below,
Swanson, CDC and RBF agree as follows:

     1.   Within  two  business days following the  execution  of
          this Agreement CDC agrees to pay to Swanson a lump  sum
          in   cash,   less  deductions  required  by   law,   of
          $2,587,500.

     2.   From  the  Effective Date and continuing until December
          1,  2001  CDC agrees to provide Swanson and his family,
          at   the  expense  of  CDC,  all  benefits  under   (or
          substantially  equivalent benefits  to)  RBF's  welfare
          benefit   plans,  practices,  policies   and   programs
          (including,  without limitation, medical, prescription,
          dental,  vision, disability, salary continuance,  group
          life  and supplemental group life and accidental  death
          insurance  plans and programs), to the extent generally
          applicable to other RBF executives.

     3.   For a period of three (3) years following the Effective
          Date (the "Restricted Period") Swanson agrees:

          (a)  Not  to  engage  in  Competition  with  CDC.   For
               purposes of this Section 3(a), "Competition" shall
               mean  Swanson  engaging in or  otherwise  being  a
               director,  officer,  employee,  principal,  agent,
               stockholder,  member,  owner  or  partner  of,  or
               permitting his name to be used in connection  with
               the   activities  of  any  corporation  or   other
               business  organization  in the  offshore  contract
               drilling    industry   in   direct   or   indirect
               competition  with CDC, its parent,  subsidiary  or
               affiliated  companies,  but  shall  not   preclude
               Swanson  from being or becoming the registered  or
               beneficial owner of up to five (5%) of  any  class
               of  capital  voting  stock (or  equivalent  voting
               interest)  of  any corporation or  other  business
               organization  in  the offshore  contract  drilling
               industry,  provided Swanson does  not  participate
               actively  in such business until the  end  of  the
               Restricted Period.

          (b)  Not to disclose to any third party not a member of
               the Company Group (as hereinafter defined), its or
               their   legal  counsel  or  independent  auditors,
               Confidential Information (as hereinafter  defined)
               or  Trade Secrets (as hereinafter defined), except
               any  of  the  Confidential  Information  or  Trade
               Secrets  which  shall be or become in  the  public
               domain  other  than by breach by  Swanson  of  his
               obligations set out in this Section 3(b) or  shall
               be  required to be disclosed by applicable laws or
               regulations,   any   judicial  or   administrative
               authority or stock exchange rule or regulation.

               For  purposes  of  this  Section  3(b):   "Company
               Group"  shall  mean  CDC, its parent  corporation,
               subsidiaries  and  affiliates;  "Confidential  In-
               formation"  shall mean (r) internal  policies  and
               procedures,   (s)   financial   information,   (t)
               marketing   strategies,  (u)  secret  discoveries,
               inventions, formulae, designs, methods,  processes
               and  know-how not constituting Trade Secrets,  and
               (v)  other non-public information relating to  the
               Company Group's business, the disclosure of  which
               would  materially  adversely  affect  the  Company
               Group's  business  or  financial  condition;   and
               "Trade Secrets" shall mean all secret discoveries,
               inventions, formulae, designs, methods,  processes
               and  know-how  entitled  to  protection  as  trade
               secrets under the laws of the state of Texas.

     4.        (a)   The  Stock Option Agreements between Swanson
               and   CDC   referred  to  below  are  respectively
               amended:   (i)  to  revise the  number  of  option
               shares  covered  by  each such  agreement  and  to
               revise  the  option exercise price  per  share  to
               reflect  the  adjustments necessary to  take  into
               account the conversion of CDC shares to shares  of
               RBF effected as a result of the merger transaction
               between CDC and RBF concluded December 1,1998, and
               (ii)  to  extend the period of time  within  which
               Swanson   shall  be  entitled  to   exercise   the
               outstanding   stock   options   granted   to   him
               thereunder, notwithstanding the provisions of such
               Stock Option Agreements, as follows:

                                        Option
Date of Agreement   No. of Options   Exercise Price   Period of Time
                                      (per share)      to Exercise

  May 22, 1996         47,600         $  8.24          May 21, 2006
  May 21, 1997         34,000           19.27          May 20, 2007
  May 13, 1998         85,000           29.71          May 12, 2008

          (b)  The Stock Option Agreement between Swanson and RBF
               dated  December 1, 1998 is amended to  remove  the
               restrictions on vesting and extend the  period  of
               time  within  which Swanson shall be  entitled  to
               exercise the outstanding stock options granted  to
               him    thereunder    to    December    1,    2008,
               notwithstanding  the  provisions  of  such   Stock
               Option Agreement.

     5.   The Agreement shall be binding upon and shall inure  to
          the   benefit   of   the  parties,   their   respective
          representatives,  agents,  attorneys,  successors   and
          assigns,  and,  in  particular,  without  limiting  the
          generality  of  the  foregoing,  to  CDC's  and   RBF's
          directors,  officers  and employees  and  to  Swanson's
          heirs,  executors, administrators, legal  and  personal
          representatives and assigns.

     6.   This  Agreement shall be deemed to be a  contract  made
          under  and governed by, the laws of the State of Texas,
          without reference to principles of conflicts of law.

     7.   The  provisions of this Agreement are severable.  If  a
          court or other tribunal of competent jurisdiction rules
          any   provision  of  this  Agreement  is   invalid   or
          unenforceable, such ruling will not affect the validity
          or   enforceability  of  any  other  provision  of  the
          Agreement,  and this Agreement shall be  deemed  to  be
          modified  and  amended so as to be enforceable  to  the
          extent permitted by law.


     This  Agreement is signed in Houston, Texas  on  July      ,
1999.


                              _______________________
                              Douglas E. Swanson



                              CLIFFS DRILLING COMPANY



                              By:____________________
                                 Its duly authorized
                                 officer


                              R&B FALCON CORPORATION



                              By:____________________
                                 Its duly authorized
                                 officer