EXECUTIVE AGREEMENT (Severance/Non-Competition)

Exhibit 10.16

EXECUTIVE AGREEMENT

(Severance/Non-Competition)

This Executive Agreement (the “Agreement”) is made as of July 1, 2004, by and between Horizon Health Corporation, a Delaware corporation (hereinafter referred to as “Horizon”), and David K. Meyercord (hereinafter referred to as “Executive”).

WHEREAS, the Executive has accepted employment as a Senior Vice President and General Counsel of Horizon; and

WHEREAS, the Executive and Horizon have agreed to enter into a severance agreement, in part, for and in consideration of the agreement of the Executive to a non-competition agreement on the terms and conditions hereinafter set forth;

In consideration of the premises and the mutual terms and conditions hereinafter set forth, Horizon and the Executive hereby agree as follows:

1. Severance Agreements. In the event of the termination of employment of the Executive by Horizon without Cause (as defined in Section 2 hereof) or the termination of employment of the Executive by the Executive with Good Reason (as defined in Section 3 hereof,

a. Executive shall be entitled to severance pay in an amount equal to the Executive’s annual base salary then in effect on the date of termination of employment plus fifty percent (50%) of the maximum annual cash bonus that the Executive was eligible to receive with respect to the fiscal year in which such termination occurs. Such severance amount shall be payable in twelve (12) equal monthly installments payable on the first regular payroll payment date of Horizon in the calendar month after the month in which such termination of employment occurs.

b. In the event such termination occurs after a Change of Control, all stock options or other equity deferred awards granted by the Company to the Executive, all contributions made by the Company for the account of the Executive to any pension, thrift or any other benefit plan, and all other benefits or bonuses (including cash bonuses) which contain vesting or exercisability provisions conditioned upon or subject to the continued employment of the Executive, shall become fully vested; provided, however, that, if any such amount, benefit, or payment cannot become fully vested pursuant to such plan or arrangement on account of limitations imposed by law, the Executive shall be entitled, to the extent permitted by law, to receive from the Company an amount in cash payable within 30 days of the date of termination equal to the total amount of benefits or payments which the Executive will have to forfeit pursuant to such plan or arrangement on account of such termination of employment.

c. The Company shall continue the participation of the Executive on the same basis as extended to senior executive officers of the Company from time to time in all life, accident, disability, medical, dental and all other health plans maintained by the Company for its

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senior executives for a period of one year commencing with the calendar month after the month in which such termination occurs. No severance pay shall be payable to the Executive in the event of (a) the voluntary termination of employment by the Executive without Good Reason, (b) the termination of employment of the Executive by Horizon with Cause or (c) the termination of employment of the Executive due to death, disability or retirement.

2. Definition of Cause. For purposes of this Agreement, the term “Cause” shall mean: (i) conviction of a crime punishable by imprisonment under state or federal law; (ii) commission of any act of dishonesty against Horizon; (iii) willful and material failure to perform the employment duties by the Executive and the continuation of such failure for at least ten days after Horizon provides written notice to the Executive specifying in reasonable detail the nature of such failure, (iv) failure by the Executive to devote substantially all his working, time and ability exclusively to the attention of Horizon; or (v) the failure of the Executive to exercise diligence to protect the trade secrets and confidential and proprietary information of Horizon.

3. Definition of Good Reason. For the purposes of this Agreement, the term “Good Reason” shall mean:

i. If the Company breaches any material provision of this Agreement or fails to perform any of its obligations hereunder, including, without limitation, the failure to timely pay any amounts due hereunder, and such breach or failure continues for at least ten days after the Executive provides written notice to the Company specifying in reasonable detail the nature of such breach or failure; or

ii. After the occurrence of a Change of Control, the Executive is required to work at an office location outside the Dallas/Ft. Worth metropolitan area; or

iii. After the occurrence of a Change of Control, the Company materially reduces the compensation of the Executive or assigns to the Executive any duties inconsistent in any respect with the Executive’s position (including status, office, title and reporting requirements), authority or responsibilities or take any other action which results in a material diminution in such position, authorities, duties or responsibilities of the Executive.

4. Definition of Change of Control. For purposes of this Agreement, “Change of Control” shall mean:

a. The acquisition by any individual, entity or group (within the meaning of Section 13(d)(3) or 14(d)(2) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”)) (an “Acquiring Person”) of beneficial ownership (within the meaning of Rule 13d-3 promulgated under the Exchange Act) of 50% or more of either (i) the then outstanding shares of common stock of the Company (the “Outstanding Company Common Stock”) or (ii) the combined voting power of the then outstanding voting securities of the Company entitled to vote generally in the election of directors (the “Outstanding Company Voting Securities”); provided, however, that for purposes of this subsection (a), the following acquisitions shall not constitute a Change of Control: (i) any acquisition directly from the Company, (ii) any acquisition by the Company, (iii) any acquisition by any employee benefit plan (or related trust) sponsored or maintained by the Company or any corporation controlled by the Company.

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b. Individuals who, as of the date hereof, constitute the Board (the “Incumbent Board”) cease for any reason to constitute at least a majority of the Board; provided, however, that any individual becoming a director subsequent to the date hereof whose election or nomination for election by the Company’s shareholders, was approved by a vote of at least a majority of the directors then comprising the Incumbent Board shall be considered as though such individual were a member of the Incumbent Board, but excluding, for this purpose, any such individual whose initial assumption of office occurs as a result of an actual or threatened election contest with respect to the election or removal of directors or other actual or threatened solicitation of proxies or consents by or on behalf of an Acquiring Person other than the Board; or

c. Approval by the shareholders of the Company of a complete liquidation or dissolution of the Company.

5. Non-Competition and Confidentiality.

a. Executive recognizes and understands that in performing the responsibilities of his employment, he will occupy a position of fiduciary trust and confidence, pursuant to which he will develop and acquire experience and knowledge with respect to the business of Horizon and its confidential proprietary information. It is the express intent and agreement of Executive and Horizon that such knowledge and experience shall be used exclusively in the furtherance of the interests of Horizon and not in any manner which would be detrimental to Horizon’s interests. Executive further understands and agrees that Horizon conducts its business within a specialized market segment throughout the United States and that it would be detrimental to the interests of Horizon if Executive used the knowledge and experience which he acquires pursuant to his employment and position with Horizon for the purpose of directly or indirectly competing with Horizon, or for the purpose of aiding other persons or entities in so competing with Horizon, anywhere in the United States.

Executive therefore agrees that so long as he is employed by Horizon and for a period of one (1) year from the date of termination of employment for any reason whatsoever, with or without Cause, (unless Executive first secures the written consent of Horizon)

i. Executive shall not, directly or indirectly, as an employee, employer, consultant, agent, principal, partner, shareholder, corporate officer, director or through any kind of ownership or investment (other than ownership of securities of publicly held corporations of which Executive owns less than four percent (4%) of any class of outstanding securities), engage in any business or render any services to any business that is in competition with the business conducted by Horizon on the date of termination of employment; and

ii. Executive shall not encourage, solicit or induce, directly or indirectly, any manager, supervisor, officer, director or employee of Horizon to terminate his or her employment with Horizon or hire any such individual.

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The foregoing non-competition provisions are not to be construed to prohibit Executive from being employed in the health care industry, but rather to permit him to be so employed so long as such employment does not involve Executive’s direct or indirect participation in a business which is the same or similar to Horizon’s business.

b. Executive acknowledges that, in rendering his services, he shall have access to and contact with the trade secrets and confidential and proprietary business information of Horizon. Both during the term of this Agreement and thereafter, Executive covenants and agrees as follows:

i. That he shall use his best efforts and exercise utmost diligence to protect and safeguard the trade secrets and confidential and proprietary information of the Company;

ii. That he shall not disclose any of such trade secrets and confidential and proprietary information, except as may be required in the course of performing his services under this Agreement; and

iii. That he shall not use, directly or indirectly, for his own benefit or for the benefit of another, any of such trade secrets and confidential and proprietary information.

All files, records, documents, memoranda, notes or other documents relating to the business of the Company, whether prepared by the Executive or otherwise coming into his possession, shall be the exclusive property of Horizon and shall be delivered to Horizon and not retained by the Executive upon termination of employment for any reason whatsoever.

It is expressly understood, however, that the foregoing shall not apply to any information that was generally available to the public in a non-confidential basis prior to the date of this Agreement or was or becomes generally available to the public on a non-confidential basis from a third-party who is not bound to keep such information confidential.

c. Executive acknowledges that the restrictions contained in Section 3 are reasonable and necessary to protect the legitimate interests of Horizon in view of the nature of the business in which Horizon is engaged. Executive understands that the remedies at law for his violations of any of the covenants or provisions of Section 3 will be inadequate, that such violation will cause irreparable injury within a short period of time, and that Horizon shall be entitled to preliminary injunctive relief against such violation and specific performance of such covenants. Such injunctive relief and specific performance shall be in addition to, and in no way in limitation of, any and all other remedies Horizon shall have in law and equity for the enforcement of those covenants and provisions.

6. General Provisions.

a. Any notice to be given hereunder by either party to the other may be effected in writing by personal delivery or by mail, registered or certified, postage prepaid with return receipt requested. Mailed notices shall be addressed to the parties at the addresses set forth below, but each party may change his or its address by written notice in accordance with

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this Section 4(a). Notice delivered personally shall be deemed communicated as of the date of actual receipt; mailed notices shall be deemed communicated as of three days after the date of mailing.

b. If any provision in this Agreement is held by a court of competent jurisdiction to be invalid, void or unenforceable, such provision shall be fully severable and the remaining provisions shall, nevertheless, continue in full force and without being impaired or invalidated in any way. Furthermore, in lieu of such invalid, void or unenforceable provision there shall be added automatically as a part of this Agreement, a provision as similar in terms to such invalid, void or unenforceable provision as may be possible and still be legal, valid and enforceable.

c. This Agreement shall be governed by and construed in accordance with the laws of the State of Texas.

d. This Agreement constitutes the sole and complete agreement of the parties, and supersedes all other agreements and understandings, whether oral or written, between the parties hereto with respect to the subject matter hereof. Each party to this Agreement acknowledges that no representations, inducements or agreements, oral or otherwise, not contained in this Agreement, and no other agreement, statement or promise not contained in this Agreement, shall be valid or binding. Any modification of this Agreement will be effective only if it is in writing signed by the parties hereto.

e. This Agreement may be executed in two or more counterparts, each of which shall constitute an original, but which together shall constitute one and the same agreement.

(Remainder of Page Intentionally Left Blank)

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IN WITNESS WHEREOF, the parties have executed this Executive Agreement as of the date first written above.

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