CAPNIA, INC. AMENDMENTNO. 1 TO CONVERTIBLE NOTE AND WARRANT PURCHASE AGREEMENT, CONVERTIBLE PROMISSORY NOTES AND WARRANTS TO PURCHASE SHARES

Exhibit 10.12

CAPNIA, INC.

AMENDMENT NO. 1 TO CONVERTIBLE NOTE AND WARRANT PURCHASE

AGREEMENT, CONVERTIBLE PROMISSORY NOTES AND

WARRANTS TO PURCHASE SHARES

This Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares (this “Amendment”) is made as of November 10, 2010, by and among Capnia, Inc., a Delaware corporation (the “Company”), with offices at 2445 Faber Place, Suite 250, Palo Alto, CA 94303 and the persons and entities who are signatories hereto (the “Investors”).

RECITALS

A. WHEREAS, the Company and the Investors are parties to that certain Convertible Note and Warrant Purchase Agreement dated as of February 10, 2010 (the “Agreement”) pursuant to which the Company sold and issued to each Investor, a convertible promissory note in the principal amount set forth opposite such Investor’s name on Exhibit A thereto (together with all such convertible promissory notes sold and issued pursuant to the Agreement, the “Notes”) together with a related warrant to purchase shares of the Company’s capital stock (together with all such warrants to purchase shares issued pursuant to the Agreement, the “Warrants”);

B. WHEREAS, Section 6.1 of the Agreement provides that the holders of at least two-thirds in interest of the Notes may, with the Company’s prior written consent, waive, modify or amend any provisions of the Agreement, the Notes and the Warrants on behalf of all Investors (as defined in the Agreement).

C. WHEREAS, the Company and the undersigned Investors wish to amend the Agreement, the Notes and the Warrants to: (i) authorize the Company to sell and issue additional Notes with an aggregate principal amount of up to $2,000,000, together with related Warrants, (ii) extend the Maturity Date of the Notes to February 10, 2012, (iii) amend the definition of Shares under the Warrants to reflect the extended Maturity Date of the Notes, and (iv) make certain other changes.

D. WHEREAS, unless otherwise stated, capitalized terms not otherwise defined herein shall have the meaning set forth in the Agreement, Notes and Warrants, as applicable.

AGREEMENT

NOW THEREFORE, in consideration of the foregoing, and the representations, warranties, and conditions set forth below, the parties hereto, intending to be legally bound, hereby agree as follows:

1. Amendments.

1.1 Amendments to Convertible Note and Warrant Purchase Agreement.

(a) The following section is inserted as a new Section 1.5 of the Agreement:

“1.5 Extension Closing.

Notwithstanding Section 1.3 of the Agreement, one or more additional subsequent Closings may take place following the Final Closing Date and on or before thirty (30) days following November 10, 2010 (each, an “Extension Closing” and also a “Closing”) at which the Company may sell and issue Notes with an aggregate principal amount of up to $2,000,000 to Investors who have participated in one or more prior Closings, or such other persons or entities acceptable to the Company. The purchase, sale and issuance of the Notes and Warrants at an Extension Closing shall be subject to all terms and conditions of this Agreement.”

(b) Section 2 of the Agreement is hereby amended and restated in its entirety to read as follows:

“2. Authorization. The Company has authorized the sale and issuance of Notes with an aggregate principal amount of up to $4,700,000 with respect to the Initial Closing and the Final Closing. The Company has authorized the sale and issuance of Notes with an aggregate principal amount of up to $2,000,000 with respect to all Extension Closings.”

1.2 Schedule of Investors. Exhibit A to the Agreement is hereby replaced in its entirety with Exhibit A to this Amendment.

1.3 Amendment to Convertible Promissory Notes. The first paragraph of each Note is hereby amended and restated in its entirety to read as follows:

“FOR VALUE RECEIVED CAPNIA, INC., a Delaware corporation (the “Company”), promises to pay to                              (the “Holder”), or its registered assigns, the principal amount of $            , or such lesser amount as shall equal the outstanding principal amount hereof, together with compound interest from the date of this Note on the unpaid principal balance at a rate equal to 12% per annum, compounded on the first day of each month and computed on the basis of the actual number of days elapsed and a year of 365 days. Two times the unpaid principal, together with any then accrued but unpaid interest and any other amounts payable hereunder, shall be due and payable on the earlier of (i) upon demand made after February 10, 2012 (the “Maturity Date”) by Holders representing at least a majority of the principal amount of all then outstanding Notes issued pursuant to that certain Convertible Note and Warrant Purchase Agreement by and among the Company and the Investors described therein, dated as of February 10, 2010, (as the same may from time to time be amended, modified or supplemented, the “Purchase Agreement”), or (ii) when, upon or after the occurrence of an Event of Default (as defined below), such amounts are declared due and payable by the Holder or made automatically due and payable in accordance with the terms of this Note. This Note is one of the “Notes” issued pursuant to the Purchase Agreement. Capitalized terms not otherwise defined herein shall have the meaning set forth in the Purchase Agreement.”

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1.4 Form of Convertible Promissory Note. Exhibit B to the Agreement is hereby replaced in its entirety with Exhibit B to this Amendment.

1.5 Amendment to Warrant to Purchase Shares. Section 1(a) of each Warrant is hereby amended and restated in its entirety to read as follows:

“(a) Definition of Shares. “Shares” shall mean Next Financing Securities in the event that a Next Financing occurs prior to February 10, 2012 (the “Note Maturity Date”) and the Holder converts the Note issued to Holder into Next Financing Securities. In the event that a Next Financing has not occurred before the Note Maturity Date, “Shares” shall mean either the Company’s Series C Preferred Stock or Next Financing Securities, whichever such securities Original Issue Price (as such term is defined in the Company’s Amended and Restated Certificate of Incorporation) is lower.”

1.6 Form of Warrant to Purchase Shares. Exhibit C to the Agreement is hereby replaced in its entirety with Exhibit C to this Amendment.

2. Miscellaneous.

2.1 Waivers and Amendments. This Amendment nor any term hereof may be amended, waived, discharged or terminated other than by a written instrument signed by the party against whom enforcement of any such amendment, waiver, discharge or termination is sought; provided, however, that the holders of at least two-thirds in interest of the Notes issued pursuant to the Agreement may, with the Company’s prior written consent, waive, modify or amend any provisions hereof on behalf of all Investors.

2.2 Governing Law. This Amendment shall be governed in all respects by the laws of the State of California as such laws are applied to agreements between California residents entered into and to be performed entirely within California.

2.3 Successors and Assigns. Except as otherwise expressly provided herein, the provisions hereof shall inure to the benefit of, and be binding upon, the successors, assigns, heirs, executors and administrators of the parties hereto.

2.4 Entire Agreement. This Amendment (including the exhibits attached hereto and the other documents delivered pursuant hereto) and, to the extent not amended hereby, the Agreement, the Notes, the Warrants and the exhibits attached thereto and the other documents delivered pursuant thereto, constitute the full and entire understanding and agreement between the parties with regard to the subjects hereof and thereof.

2.5 Counterparts. This Amendment may be executed in any number of counterparts, each of which shall be an original, but all of which together shall be deemed to constitute one instrument.

2.6 Facsimile Execution and Delivery. A facsimile or other reproduction of this Amendment may be executed by one or more parties hereto and delivered by such party by facsimile or any similar electronic transmission device pursuant to which the signature of or on behalf of such party can be seen. Such execution and delivery shall be considered valid, binding and effective for all purposes. At the request of any party hereto, all parties hereto agree to execute and deliver an original of this Amendment as well as any facsimile, telecopy or other reproduction hereof.

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2.7 Waiver of Anti Dilution Adjustment. The undersigned Investors who are the holders of the requisite outstanding shares of Preferred Stock, on behalf of themselves and all other holders of Preferred Stock, hereby waive any price-based anti-dilution adjustment under Article V, Section 3(D) of the Restated Certificate with respect to the Company’s sale and issuance of the Securities pursuant to the Agreement, as hereby amended.

2.8 Waiver of Right of First Refusal. Pursuant to Section 4.2 of the Rights Agreement, the undersigned Investors, who are the holders of at least two-thirds of the Registrable Securities (as defined in the Rights Agreement), on behalf of themselves and all other holders of Registrable Securities granted the right of first offer pursuant to Section 2.3 of the Rights Agreement, hereby agree to waive such right of first offer and any notice requirement contained therein with respect to the Company’s sale and issuance of the Securities pursuant to the Agreement, as hereby amended.

(signature page follows)

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IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

IN WITNESS WHEREOF, the parties have caused this Amendment No. 1 to Convertible Note and Warrant Purchase Agreement, Convertible Promissory Notes and Warrants to Purchase Shares to be duly executed and delivered by their proper and duly authorized officers as of the date and year first written above.

[Signature Page to Amendment No. 1 to Convertible Note and Warrant Purchase Agreement,

Convertible Promissory Notes and Warrants to Purchase Shares]

EXHIBIT A

Schedule of Investors

A-1

A-2

EXHIBIT B

Form of Convertible Promissory Note

EXHIBIT C

Form of Warrant to Purchase Shares