The invention relates to a master cylinder (1) with reduced free travel (23). Current master cylinders have a free travel during the displacement of a piston (6) in a bore (5) of a master cylinder body (3). Such a free travel may be reduced with the aid of a frustoconical portion (24) in the piston, an orifice (14) for communication of hydraulic fluid being situated on said inclined wall, a gap (26) between the inclined wall and an inner wall (12) of the bore allowing a passage for hydraulic fluid capable of filling a pressure chamber (4). However, such inclined walls create a change in the slope of an outer wall (29) of the piston, this change being able to cause a separation of an inner lip (19) of a sealing cup (17). To prevent this separation, the invention provides that the inclined wall forms a convex rounded surface (32).