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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  SCHEDULE 14A

          Proxy Statement Pursuant to Section 14(a) of the Securities
                     Exchange Act of 1934 (Amendment No.  )

Filed by the Registrant [X]
Filed by a Party other than the Registrant [ ]

Check the appropriate box:

[ ]  Preliminary Proxy Statement
[ ]  CONFIDENTIAL, FOR USE OF THE COMMISSION ONLY (AS PERMITTED BY
     RULE 14a-6(e)(2))
[ ]  Definitive Proxy Statement
[X]  Definitive Additional Materials
[ ]  Soliciting Material Pursuant to Section 240.14a-12

                                Transocean Inc.
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                (Name of Registrant as Specified In Its Charter)

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    (Name of Person(s) Filing Proxy Statement, if other than the Registrant)

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[X]  No fee required.

[ ]  Fee computed on table below per Exchange Act Rules 14a-6(i)(4) and 0-11.

     1) Title of each class of securities to which transaction applies:

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        pursuant to Exchange Act Rule 0-11 (set forth the amount on which the
        filing fee is calculated and state how it was determined):

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[ ]  Fee paid previously with preliminary materials.

[ ]  Check box if any part of the fee is offset as provided by Exchange Act
     Rule 0-11(a)(2) and identify the filing for which the offsetting fee was
     paid previously. Identify the previous filing by registration statement
     number, or the Form or Schedule and the date of its filing.

     1) Amount Previously Paid:

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     2) Form, Schedule or Registration Statement No.:

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SEC 1913 (02-02)



                          SUPPLEMENT TO PROXY STATEMENT
                  FOR ANNUAL GENERAL MEETING OF TRANSOCEAN INC.
                                  MAY 13, 2004

         The following information, being mailed to shareholders on or about
March 29, 2004, supplements and amends the notice of the 2004 annual general
meeting of shareholders and the accompanying proxy statement, each dated March
19, 2004, furnished in connection with the solicitation of proxies by the board
of directors of Transocean Inc. for use at its annual general meeting to be held
on Thursday, May 13, 2004 at 9:00 a.m., at the Royal Pavilion Hotel, St. James,
Barbados.

         The information contained in this supplement should be read in
conjunction with the proxy statement. There is no change in the time or place of
the annual general meeting or the record date to determine shareholders entitled
to notice of and to vote at the annual general meeting.

         In early 2004, the board of directors began seeking to identify
potential director candidates in an effort to add independent directors to the
board. At the time of its last meeting, the board had identified one such
candidate, Mr. Robert M. Sprague, who has been nominated for election to the
board at the upcoming annual general meeting. In connection with the board's
current search efforts to add an independent director in addition to Mr.
Sprague, it has identified potential director candidates and is in the process
of conducting its normal investigation relative to the background and
qualifications of certain of these individuals. After the printing of our proxy
statement, it was determined that the investigation process would likely be
completed for one or more of the individuals prior to the meeting of the board
of directors following the annual general meeting.

         If this investigation process is concluded as anticipated, it is
expected that the board will consider increasing the size of the board from 11
to 12 at this upcoming meeting and appointing one of these potential candidates
to fill the new board seat resulting from the increase in board size. If a
director were to be appointed, it is expected that the director would be placed
in the class of directors with terms expiring in 2005. The candidates currently
under consideration were initially identified by a search firm retained by the
Corporate Governance Committee. The search firm is assisting us in identifying
potential board candidates, interviewing those candidates and conducting
investigations relative to their background and qualifications.