Confidential Treatment Requested by Fluidigm Corporation

Exhibit 10.5A

ADDENDUM TO

SECOND AMENDED AND RESTATED LICENSE AGREEMENT

THIS ADDENDUM TO SECOND AMENDED AND RESTATED LICENSE AGREEMENT (this “Addendum”) dated as of March 29, 2007 (the “Addendum Date”), is entered into between CALIFORNIA INSTITUTE OF TECHNOLOGY (“Caltech”), having an address at 1200 East California Boulevard, Pasadena, California 91125, and FLUIDIGM CORPORATION (“Licensee”), having a principal place of business at 7100 Shoreline Court, South San Francisco, California 94080, with respect to the following facts:

A. The parties entered into the Second Amended and Restated License Agreement (the “Agreement”) effective May 1, 2000, with a second restatement date as of May 1, 2004. All terms used, but not defined herein, shall have the respective meanings set forth in the Agreement.

B. On the terms and conditions of this Addendum, the parties desire to clarify and modify certain provisions to the Agreement.

NOW, THEREFORE, in consideration of the foregoing premises and the mutual covenants set forth below, the parties agree as follows:

1. Licensed Patents and Improvements .

1.1 The Agreement is amended by deleting Exhibit A to the Agreement and by replacing it with Exhibit A to this Addendum.

1.2 Caltech represents that it has disclosed to Licensee all Improvements arising prior to the Addendum Date.

1.3 The parties acknowledge that Exhibit A to this Addendum includes (a) all Improvements disclosed by Caltech to Licensee prior to the Addendum Date, and elected by Licensee to be included in the scope of the license grant by Caltech to Licensee under the Agreement, and (b) all updates on all Licensed Patents as of the Addendum Date. Caltech confirms that Licensee has taken all action on its part that is necessary for all subject matter included in Exhibit A to this Addendum to be included in the scope of the license grant by Caltech to Licensee under the Agreement.

2. Licensee Equity Interest and Improvement Periods .

2.1 Notwithstanding anything to the contrary in Article 5 of the Agreement, the Improvement Periods shall be those periods from June 1, 2003 through May 31, 2004, from June 1, 2004 through May 31, 2005, from [***]

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Confidential Treatment Requested by Fluidigm Corporation

2.2 Notwithstanding anything to the contrary in Article 5 of the Agreement, (a) Licensee shall issue to Caltech [***] [***] shares of common stock of Licensee, pursuant to the terms of a reasonable and customary stock issuance agreement, and (b) the parties acknowledge that the issuance of such shares (in addition to the shares issued by Licensee to Caltech prior to the Second Restatement Date) shall be in full satisfaction of Licensee’s obligations to issue shares or otherwise make payments to Caltech pursuant to the Agreement.

3. Royalty Reports .

The parties acknowledge (a) that the royalty reports received by Caltech under Section 9.2 of the Agreement prior to the Addendum Date are presumed correct and not subject to challenge, audit or amendment, and (b) that the format of, and the methodology used by Licensee in preparing, the royalty reports under Section 9.2 of the Agreement are mutually acceptable and in compliance wi