RETENTION BONUS AGREEMENT

Exhibit 10.4

RETENTION BONUS AGREEMENT

This RETENTION BONUS AGREEMENT (this “Agreement”), dated as of April 5, 2012 (the “Effective Date”), is by and among Amedisys, Inc., a Delaware corporation (“Amedisys”), Amedisys Holding, L.L.C., a Louisiana limited liability company (“Holding,” and, collectively with Amedisys, the “Company”), and David R. Bucey, an individual residing in the State of Louisiana (the “Executive”).

W I T N E S S E T H :

WHEREAS, the Company desires to offer the Executive a retention bonus (the “Retention Bonus”) as an incentive for the Executive to remain in the employment of the Company, upon the terms and conditions hereinafter set forth.

NOW, THEREFORE, in consideration of the mutual covenants and promises contained herein and for good and valuable consideration, the receipt of which is hereby acknowledged, the parties hereto, each intending to be legally bound hereby, agree as follows:

1. Certain Capitalized Terms. Capitalized terms used but undefined herein shall have the meanings assigned to them in the Employment Agreement dated July 27, 2010 by and among Amedisys, Holding and the Executive (as amended by the First Amendment thereto dated January 3, 2011) (as so amended, the “Employment Agreement”).

2. Retention Bonus.

(a) Payment. The Retention Bonus shall be paid by the Company (in accordance with its normal payroll practices) to the Executive in a lump sum (less applicable withholdings and payroll deductions) within fifteen (15) days of the Effective Date of this Agreement, provided that the Executive remains employed by the Company as of the actual payment date.

(b) Amount. The amount (the “Amount”) of the Retention Bonus shall be Thirty-Two Thousand, Five Hundred Dollars ($32,500).

3. Repayment Obligations.

(a) If prior to April 1, 2013, (i) the Company terminates the Executive’s employment for Cause or (ii) the Executive voluntarily terminates his employment without Good Reason, the Executive will be obligated to repay 100% of the Retention Bonus Amount (as calculated before taking into account any amounts required to be withheld for taxes on the payment date or any payment date payroll deductions, as required by any Company compensation, pension or welfare benefit plan), in cash, within five (5) business days after written demand is made therefor by the Company (in accordance with the instructions contained therein).

(b) If on or after April 1, 2013 but before April 1, 2014, (i) the Company terminates the Executive’s employment for Cause or (ii) the Executive voluntarily terminates his employment without Good Reason, the Executive will be obligated to repay 66.67% of the Retention Bonus

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Amount (as calculated before taking into account any amounts required to be withheld for taxes on the payment date or any payment date payroll deductions, as required by any Company compensation, pension or welfare benefit plan), in cash, within five (5) business days after written demand is made therefor by the Company (in accordance with the instructions contained therein).

(c) If on or after April 1, 2014 but on or before April 1, 2015, (i) the Company terminates the Executive’s employment for Cause or (ii) the Executive voluntarily terminates his employment without Good Reason, the Executive will be obligated to repay 33.33% of the Retention Bonus Amount (as calculated before taking into account any amounts required to be withheld for taxes on the payment date or any payment date payroll deductions, as required by any Company compensation, pension or welfare benefit plan), in cash, within five (5) business days after written demand is made therefor by the Company (in accordance with the instructions contained therein).

(d) If after April 1, 2015, (i) the Company terminates the Executive’s employment for Cause or (ii) the Executive voluntarily terminates his employment without Good Reason, the Executive will have no obligation to repay the Retention Bonus Amount.

4. Death, Disability or Retirement. For purposes of clarification, the repayment obligations described in Section 3, above, shall not be triggered if the Executive’s employment is terminated (i) due to his death or Disability or (ii) upon his Retirement.

5. General.

(a) Withholding; Payroll Deductions. The Retention Bonus payable to the Executive shall be subject to applicable (i) taxes and withholding, as required by law, and (ii) payroll deductions, as required by any Company compensation, pension or welfare benefit plan.

(b) Severance and Other Benefits. This Agreement shall not affect the Executive’s eligibility or entitlement to receive nor shall it reduce benefits payable to the Executive under any severance, change of control or similar plan, policy or agreement with the Company, including but not limited to the Employment Agreement.

(c) Non-Salary Compensation. The parties represent, acknowledge and agree that the Retention Bonus constitutes non-salary compensation.

(d) Other Rights. This Agreement does not create any employment rights not specifically set forth in the Employment Agreement.

(e) Entire Agreement. This Agreement and the Employment Agreement contain the entire understanding of the Company and the Executive with respect to the subject matter hereof.

(f) Amendment. This Agreement may be amended or revised only by written agreement signed by an authorized officer of the Company and the Executive.

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(g) Applicable Law. This Agreement shall be construed and enforced in accordance with the laws of the State of Louisiana, without giving effect to the principles of conflict of laws thereof. The Company and the Executive hereby consent and irrevocably submit to the jurisdiction of any or all of the following courts for purposes of resolving any dispute under this Agreement: (i) the United States District Court for the Middle District of Louisiana or (ii) the Nineteenth Judicial District Court for the Parish of East Baton Rouge, State of Louisiana. The parties hereto agree that to the extent permitted, any lawsuit involving a dispute under this Agreement shall be filed and may proceed only in these referenced courts. The Company and the Executive hereby waive, to the fullest extent permitted by applicable law, any jurisdictional, venue or inconvenient forum objection which it or he may now or hereafter have to these referenced courts. The Company and the Executive further agree that any service of process or notice requirements in any such proceeding shall be satisfied if the rules of such court relating thereto have been substantially satisfied.

(h) Section 409A. The Company intends that the Retention Bonus is not compensation paid under a “nonqualified deferred compensation plan” within the meaning of section 409A of the Internal Revenue Code of 1986, as amended (“Section 409A”).

(i) Counterparts. This Agreement may be executed in two or more counterparts, all of which taken together shall constitute one instrument.

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IN WITNESS WHEREOF, the parties hereto, intending to be legally bound, have hereunto executed this Agreement as of the day and year first written above.

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