FIRST AMENDMENT TO THE HEALTH CARE PROPERTY INVESTORS, INC. SECOND AMENDED AND RESTATED

Exhibit 10.5.1

FIRST AMENDMENT TO THE

HEALTH CARE PROPERTY INVESTORS, INC.

SECOND AMENDED AND RESTATED

DIRECTOR DEFERRED COMPENSATION PLAN

Health Care Property Investors, Inc., a Maryland corporation (the “Company”), has adopted by written consent the Second Amended and Restated Director Deferred Compensation Plan (the “Plan”) effective as of the termination of the Retirement Plan for Outside Directors (the “Retirement Plan”).

In order to amend the Plan to reflect certain changes in the events and duration of distribution of the retirement benefits accumulated under the Retirement Plan, this Amendment to the Plan has been adopted by a written consent of the Board of Directors of the Company, effective as of the termination of the Retirement Plan.

1. Section 5(a)(ii) of the Plan is amended to read, in its entirety, as follows:

(ii) Retirement from the Board; or

2. The first paragraph of Section 7(a) of the Plan is amended to read, in its entirety, as follows:

(a) Interest Rate Account: Amounts credited to the Retirement Benefits Interest Rate Account, together with accumulated interest, will be distributed to the Participant in a lump sum or in any number of approximately equal annual installments, in either case as set forth in such Participant’s election in the form set forth as Exhibit A-2 hereof. In the case of distributions to be made in installments, the amount of each distribution payment shall be equal to the balance in such Interest Rate Account of as of such payment date multiplied by a fraction, the numerator of which is one, and the denominator of which is the number of installments yet to be paid to the Participant.

3. The first paragraph of Section 7(b) of the Plan is amended to read, in its entirety, as follows:

(b) Stock Credit Account: Distribution of a Participant’s Retirement Benefits Stock Credit Account shall be made in cash to the Participant in a lump sum or in any number of approximately equal annual installments, in either case as set forth in such Participant’s election in the form set forth as Exhibit A-2 hereof. In the case of distributions to be made in installments, the amount of each distribution payment shall be the cash equivalent equal to the Average Closing

Price as of such payment date multiplied by the number of credited units to be distributed for such payment. The number of credited units to be distributed shall equal the credited unit balance of the Participant’s Retirement Benefits Stock Credit Account multiplied by a fraction, the numerator of which is one, and the denominator of which is the number of installments yet to be paid to the Participant.

4. The first paragraph of Exhibit A-2 of the Plan is amended to read, in its entirety, as follows:

Pursuant to the terms of the Second Amended and Restated Director Deferred Compensation Plan (the “Plan”) of Health Care Property Investors, Inc. (the “Company”) adopted by unanimous written consent of the Board of Directors as of March 11, 1997, I hereby consent to (1) the valuation of my accrued benefits under the Company’s Retirement Plan for Outside Directors (the “Retirement Plan”) as set forth beside my name on Attachment I attached hereto, and (2), effective upon the stockholders’ approval of the amendments to the Company’s Amended and Restated Directors Stock Incentive Plan proposed in the proxy for the annual meeting of April 23, 1997, the transfer of my accrued benefits under the Retirement Plan to my Retirement Benefits Accounts under the Plan and the amendments to the Amended and Restated Director Deferred Compensation Plan, as memorialized in the Plan.

5. Exhibit A-2 of the Plan is amended to add a paragraph after the second full paragraph that shall read as follows:

I hereby specify that my accrued benefits under the Retirement Plan be paid in ¨ a lump sum or                      (check the box or enter a number) annual installments in connection with Sections 5 and 7 of the Plan.

A-2