HORIZON PHARMA, INC. AMENDMENT TO INVESTORS RIGHTS AGREEMENT

Exhibit 10.4

HORIZON PHARMA, INC.

AMENDMENT TO

INVESTORS’ RIGHTS AGREEMENT

THIS AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT (this “Amendment”) is entered into as of February 22, 2012, by and among HORIZON PHARMA, INC., a Delaware corporation (the “Company”) and the Investors. Capitalized terms used and not otherwise defined herein shall have the meanings set forth in that certain Investors’ Rights Agreement, dated as of April 1, 2010 (the “Investors’ Rights Agreement”).

RECITALS

WHEREAS, the Company and the Investors are parties to the Investors’ Rights Agreement;

WHEREAS, in connection with a credit facility with certain lenders named on Annex I hereto to be entered into on or about the date of this Amendment (the “Financing”), the Company will issue warrants to such lenders (the “Warrant Holders”) to purchase up to an aggregate of [2,835,000] shares of Common Stock (together, the “Warrants”); and

WHEREAS, as a condition to the Financing, the Company has agreed to grant the Warrant Holders certain registration rights with respect to the Common Stock issuable upon exercise of the Warrants, and the Company and the Investors desire to amend the Investors’ Rights Agreement as provided hereunder to provide such registration rights to the Warrant Holders.

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants and conditions contained herein and other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties to this Amendment hereto agree as follows:

AMENDMENT

1. Each undersigned holder of Registrable Securities, on behalf of itself and all other holders of Registrable Securities, hereby consents to the addition of each of the Warrant Holders as an “Investor” and a “Holder” under the Investors’ Rights Agreement for purposes of Section 1 thereof.

2. Section 1.1(k) of the Investors’ Rights Agreement is hereby amended and restated in its entirety as set forth below:

“(k) “Registrable Securities” means (i) the shares of Common Stock issuable or issued upon conversion of the Series A or Series B Preferred Stock, together with any other shares of capital stock of the Company hereafter acquired by any Holder, in each case held by a Holder or any assignee thereof in accordance with Section 1.12 of this Agreement; (ii) the Common Stock held by the Investors as of the date of this Agreement, together with any other shares of Common Stock of the Company issued as (or issuable upon the conversion or exercise of any warrant, right or other security which is issued as) a dividend or other distribution with respect to, or in exchange for or in

replacement of, such shares of Common Stock; and (iii) the Common Stock issued or issuable upon exercise of the Warrants or upon conversion of securities convertible into Common Stock issued or issuable upon exercise of the Warrants; excluding, however, in all cases any Registrable Securities sold in a transaction in which the rights under this Agreement are not assigned, or any shares for which registration rights have terminated pursuant to Section 1.15 of this Agreement;”

3. A new Section 1.1(p) is hereby added to the Investors’ Rights Agreement as set forth below:

“(p) “Warrants” shall mean the warrants originally issued by the Company to each of the Warrant Holders to purchase up to an aggregate of [2,835,000] shares of Common Stock at an exercise price of $0.01 per share, and any subsequent warrants issued in replacement or in substitution thereof; and”

4. A new Section 1.1(q) is hereby added to the Investors’ Rights Agreement as set forth below:

“(q) “Warrant Holders” shall mean the holders of the Warrants from time to time, provided that with respect to any transfer of Warrants, that the related rights pursuant to Section 1 of this Agreement have also been validly transferred in accordance with Section 1.12.”

5. Section 1.2(a) of the Investors’ Rights Agreement is hereby amended and restated in its entirety as set forth below:

“(a) If the Company shall receive a written request from the Holders of the lesser of (i) 30% of the Registrable Securities or (ii) 2,000,000 shares of Registrable Securities (subject to adjustment for stock splits, stock dividends, combinations, reclassifications or the like) (the “Initiating Holders”) that the Company file a registration statement under the Securities Act covering the registration of Registrable Securities with an anticipated aggregate offering price of at least $10,000,000, then the Company shall, within 20 days after receiving such request, give written notice of such request to all Holders and shall, subject to the limitations of subsection 1.2(b), use all commercially reasonable efforts to cause to be registered under the Securities Act all of the Registrable Securities that each such Holder has requested to be registered within 20 days after the mailing of such notice by the Company.”

6. Section 1.13 of the Investors’ Rights Agreement is hereby amended and restated in its entirety as set forth below:

“1.13 Limitations on Subsequent Registration Rights. The Company shall not, without the prior written consent of the Holders of at least 66 2/3% of the Registrable Securities then outstanding, enter into any agreement with any holder or prospective holder of any securities of the Company (i) that grants to such holder or prospective holder any registration rights that are senior to or have a preference on registration over the registration rights held by the Holders pursuant to this Agreement or (ii) which would

2.

allow such holder or prospective holder (a) to include any of such securities in any registration filed under Section 1.2 or 1.4 hereof or (b) to make a demand registration, other than Excluded Registrations.”

7. Section 3.5 of the Investors’ Rights Agreement is hereby amended and restated in its entirety as set forth below:

“3.5 Amendments and Waivers. Any term of this Agreement may be amended or waived only with the written consent of the Company and the holders of at least 66 2/3% of the Registrable Securities then outstanding; provided, however, that any amendment, modification or waiver of any section which adversely affects the Warrant Holders in a manner differently than other holders of Registrable Securities shall require the written consent of the Warrant Holders holding at least 66 2/3% of the Registrable Securities then issuable upon exercise of any unexercised Warrants held by all Warrant Holders. Notwithstanding the foregoing, this Agreement may be amended with only the written consent of the Company for the sole purpose of including future Warrant Holders who are transferees of the Warrants as “Investors” and “Holders”. Any amendment or waiver effected in accordance with this paragraph shall be binding upon each party to the Agreement, whether or not such party has signed such amendment or waiver, each future holder of all such Registrable Securities, and the Company.”

8. Except as modified by this Amendment, the Investors’ Rights Agreement shall remain in full force and effect in accordance with its terms.

9. This Amendment may be executed in any number of counterparts, each of which shall be an original, but all of which together shall constitute one instrument. Facsimile signatures shall be as effective as original signatures.

10. This Amendment shall be governed by and construed in accordance with the laws of the State of Delaware, without giving effect to principles of conflicts of laws.

3.

The parties have executed this Amendment to Investors’ Rights Agreement as of the date first written above.

[SIGNATURE PAGE TO AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT]

The parties have executed this Amendment to Investors’ Rights Agreement as of the date first written above.

[SIGNATURE PAGE TO AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT]

The parties have executed this Amendment to Investors’ Rights Agreement as of the date first written above.

[SIGNATURE PAGE TO AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT]

The parties have executed this Amendment to Investors’ Rights Agreement as of the date first written above.

[SIGNATURE PAGE TO AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT]

The parties have executed this Amendment to Investors’ Rights Agreement as of the date first written above.

[SIGNATURE PAGE TO AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT]

The parties have executed this Amendment to Investors’ Rights Agreement as of the date first written above.

[SIGNATURE PAGE TO AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT]

The parties have executed this Amendment to Investors’ Rights Agreement as of the date first written above.

[SIGNATURE PAGE TO AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT]

The parties have executed this Amendment to Investors’ Rights Agreement as of the date first written above.

[SIGNATURE PAGE TO AMENDMENT TO INVESTORS’ RIGHTS AGREEMENT]

ANNEX I

BPC Opportunities Fund LP

Beach Point Total Return Master Fund, L.P.

Beach Point Select Master Fund, L.P.

Royal Mail Pension Plan

Quaker BioVentures II, L.P.

FHP Pharma, L.L.C.