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

Exhibit 10.5.2

SECOND 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 as amended by that First Amendment to the Second Amended and Restated Director Deferred Compensation Plan (the “Plan”).

In order to amend the Plan to provide for more level payouts and to change the frequency for which elections to transfer amounts between the interest rate account and the dividend account can be made, this Amendment to the Plan has been adopted by the Board of Directors of the Company as of July 17, 1997.

1. Sections 3(f)(ii) and (iii) of the Plan are amended to read, in their entirety, as follows:

(ii) Participants may at any time, but not more often than once during any six (6) month period, file with the Company an election to reallocate all or any portion of amounts credited to Plan Accounts from Interest Rate Accounts to Stock Credit Accounts or vice versa. Such reallocation shall be made by the delivery to the Company by the Participant of a written election, substantially in the form of Exhibit A-3 attached, executed by the Participant which shall become effective (1) only upon the approval of the Committee in its sole discretion and (2) as of the first day of the fiscal quarter beginning immediately following the date on which the Committee approves such election or the beginning of such later fiscal quarter as may be designated in the notice.

(iii) Participants may at any time, but not more often than once during any six (6) month period, by written notice filed with the Company change the account to which future deferrals shall be credited. Any such change shall become effective on the first day of the fiscal quarter beginning immediately following the date on which the Company receives such notice, or at the beginning of any later fiscal quarter as may be designated in such notice.

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 quarterly 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 calculated to produce, utilizing reasonable assumptions concerning applicable interest rates and to the extent reasonably possible, equal payments over the distribution period.

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 quarterly 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 be calculated to produce, utilizing reasonable assumptions concerning stock price and dividend rates and to the extent reasonably possible, equal credited units over the distribution period.

EXHIBIT A-3

HEALTH CARE PROPERTY INVESTORS, INC.

NOTICE OF ELECTION TO TRANSFER DEFERRED COMPENSATION

OR BENEFITS ACCOUNTS AMOUNTS

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     , 1997, I hereby elect to reallocate the crediting of my account balance in the Plan. Of the amounted credited to my ¨ Deferred Compensation Accounts or ¨ Retirement Benefits Accounts (check one) under the Plan,                      (enter “all” or “none” or state dollar amount or state percentage) shall be invested in the Interest Rate Account, the remainder, if any, shall be invested in the Stock Credit Account, as provided for in Section 3 of the Plan. All transferred amounts shall be subject to the terms and conditions of the Plan.

A-3-1