Exhibit 10.32
AMENDMENT NO. 2 TO THE
NOBLE DRILLING CORPORATION
RETIREMENT RESTORATION PLAN
     Pursuant to the provisions of Section 7 thereof, the Noble Drilling
Corporation Retirement Restoration Plan (the “Plan”) is hereby amended in the
following respects only:
     FIRST: The last sentence of Section 4 of the Plan is hereby amended by
restatement in its entirety to read as follows:
For purposes of this Plan, (i) the value of benefits and the amounts payable
under alternate forms of benefits shall be determined using the actuarial
assumptions being used under the Retirement Plan for such purposes, and (ii) the
portion of James C. Day’s salary that is paid to him in the form of shares of
Noble Drilling Corporation common stock or ordinary shares of Noble Corporation
shall be included in the compensation that is taken into account in determining
the amount of benefits payable to or with respect to Mr. Day under the Plan.
     SECOND: Section 5 of the Plan is hereby amended by restatement in its
entirety to read as follows:
     Section 5. Payment of Benefits. The benefits payable to a Participant or
beneficiary of a Participant under this Plan shall be paid or commence being
paid, as the case may be, concurrently with the payment or the commencement of
the payment of benefits to such Participant or beneficiary under the Retirement
Plan, and shall be paid to such Participant or beneficiary in cash (i) in a
single lump sum payment, (ii) in installments over a period of up to five years,
or (iii) in any form provided for under the Retirement Plan, such form of
distribution to be determined by the Committee in its absolute discretion.
     IN WITNESS WHEREOF, this Amendment has been executed by Noble Drilling
Corporation on behalf of all Employers on this 28th day of June, 2004, to be
effective as of July 1, 2004.

                  NOBLE DRILLING CORPORATION    
 
           
 
  By:   /s/ JULIE J. ROBERTSON
 
Title: Senior Vice President — Administration