a braking device and a method of manufacture of such a braking device . the braking device has a booster formed of a cover and of a cylinder . a central orifice is formed on the cylinder . a master cylinder has a body that partially enters the booster via the central orifice . the master cylinder is fixed to the cylinder of the booster by plastic deformation of a hollow shaft . the hollow shaft borders the central orifice and extends towards the outside of the envelope and penetrates at least one orifice made in an exterior surface of the body of the master cylinder . the cylinder has a flat face that surrounds the central orifice such that a flange extends radially towards the outside of the body of the master cylinder and bears more or less flat against the flat face of the cylinder .