Corcept Therapeutics Incorporated 149 Commonwealth Drive Menlo Park, CA 94025

Exhibit 10.4

Corcept Therapeutics Incorporated

149 Commonwealth Drive

Menlo Park, CA 94025

August 1, 2013

Produits Chimiques Auxiliaires et de Synthese SA (“PCAS”)

23 Rue Bossuet

91161 Longjumeau Cedex

France

Attn. Don LaFerle

Re: Extension of Manufacturing and Supply Agreement

Dear Don,

On behalf of Corcept Therapeutics Inc. (“Corcept”), I propose amending the Manufacturing and Supply Agreement between Corcept and PCAS dated November 3, 2006 (the “Agreement”) as follows:

The language of Section 9.1 (Term) of the Agreement will be deleted in its entirety and replaced with the following text: “This Agreement shall become effective on November 3, 2006 and shall terminate on September 30, 2013.”

Our purpose in proposing this change is to make sure we have an effective contract in place during the next few months while we work the details of a successor agreement.

If this amendment to the Agreement is acceptable to PCAS, please sign and date in the space provided and return a copy to me. Please let me know if you have questions.

Approved: