AMENDMENT TO THE ROWAN COMPANIES, INC. RESTATED 1988 NONQUALIFIED STOCK OPTION PLAN

Exhibit 10.9

AMENDMENT TO THE

ROWAN COMPANIES, INC.

RESTATED 1988 NONQUALIFIED STOCK OPTION PLAN

WHEREAS, the board of directors of Rowan Companies, Inc., a Delaware corporation (the “Company”), assumed and adopted the Rowan Companies, Inc. Restated 1988 Nonqualified Stock Option Plan effective April 24, 1998 (which, as previously amended from time to time, is referred to herein as the “Plan”);

WHEREAS, the stockholders of the Company approved and adopted, at the Special Meeting of the Stockholders on April 16, 2012, the Agreement and Plan of Merger and Reorganization (the “Merger Agreement”) by and between the Company and a newly formed Delaware limited liability company and wholly owned subsidiary of Rowan Delaware (“Rowan Mergeco”), pursuant to which Rowan Mergeco will merge with and into the Company (the “Merger”), with the Company surviving the merger as an indirect, wholly owned subsidiary of Rowan Companies plc, a newly formed public limited company incorporated under English law (“Rowan UK”);

WHEREAS, pursuant to the Merger Agreement, each outstanding share of common stock of the Company will be converted, on a one-for-one basis, into the right to receive a Class A Ordinary Share in Rowan UK;

WHEREAS, pursuant to the Merger Agreement, outstanding equity awards relating to shares of common stock of the Company granted to employees and directors by the Company under the Company’s equity incentive plans (including the Plan) prior to the effective time of the Merger will entitle the holder of such equity award to purchase, acquire or receive, or receive benefits or amounts based on, as applicable, an equal number of Shares (as defined below); and

WHEREAS, the board of directors of the Company has determined it is desirable to adopt this amendment to the Plan, contingent upon the consummation of the Merger and to be effective as of May 4, 2012 (or, if different, the effective date of the Merger), to reflect the provisions of the Merger Agreement and the effect of the Merger on the Plan and any awards outstanding under the Plan.

NOW, THEREFORE, BE IT RESOLVED that, contingent upon the consummation of the Merger and effective as of May 4, 2012 (or, if different, the effective date of the Merger), the Plan is amended as follows:

“Rowan UK” means Rowan Companies plc, a public limited company incorporated under English law.

“Share” means a Class A ordinary share of Rowan UK, nominal value $0.125.

The Plan shall be administered by a committee (the “Committee”) of, and appointed by, the board of directors or Rowan UK (the “Board”).

Such Shares (x) may consist of newly allotted and issued Shares, Shares that have been acquired by the trustees of an employee benefit trust established in connection with the Plan, or Shares acquired on the open market and (y) shall be fully paid and nonassessable.

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