Brake master cylinder (10) for a motor vehicle, of the type which comprises a substantially axial body (12) inside a bore (14) of which is slideably mounted at least one axial piston, of the type in which the bore (14) comprises two seals, front and rear, interposed between the piston and the bore (14), characterized in that it comprises at least one wide groove (66, 68) which is formed in the bore (14) in front of a groove (70, 72) for retaining the front seal, which extends at least in part around the piston, and which communicates with said retaining groove (70, 72) and the hole in the piston, in order to allow resupplies to occur with a high flow rate.