Booster brake device with concealed travel

A boosted brake device for a motor vehicle, comprising a master cylinder filled with a brake fluid and having a main hydraulic piston intended to receive an actuation force composed of an input force and a booster force both acting in an axial direction, and a pneumatic booster capable of being activated by applying the input force to a control rod for opening a valve in order to exert the actuation force on the main hydraulic piston, the booster comprising a rigid casing separated in leaktight fashion into two chambers by means of at least one movable partition, capable of being stressed by a pressure difference between the two chambers resulting from opening the valve and of driving a pneumatic piston which can move with respect to the casing, carrying said valve and contributing at least to transmitting said booster force, the main hydraulic piston of the master cylinder comprising a hollow movable cylinder communicating with the master cylinder, receiving at least part of the booster force, and inside which slides, in leaktight fashion and in the axial direction, a secondary hydraulic piston capable of receiving at least said input force, characterized in that the movable partition is mounted slidingly on the pneumatic piston so as to be able to slide with respect to the pneumatic booster in the direction of the master cylinder from an initial relative position in the movable partition which abuts against the pneumatic piston in a direction opposite from the master cylinder, and in that the movable partition, when stressed by a pressure difference, presses at least indirectly on the movable cylinder in the direction of the master cylinder.