A braking system comprising a master cylinder (48) comprising at least one variable-volume chamber and one moving piston (207), movement of which causes the volume of said chamber to vary, characterized in that said master cylinder further comprises means (217) of connection to a source (116) of pressurized brake fluid including a second master cylinder including a variable-volume chamber (84.2) and a piston (86) driven, on demand from an electronic control unit (5), by an actuator (88), said chamber (84.2) of said second master cylinder being connected by said means of connection (217) to said chamber of said master cylinder (48), and a variable-volume second chamber (84.1) connected by a connection (213) to a hydraulic brake boosting means (72).