The invention concerns a device comprising first and second brake means (16, 20) respectively integral with the first and second element (10, 12) in rotation about an axis of rotation (14), and a brake piston (18) capable of taking up an active braking position to prevent the relative rotation of the two elements and an inoperative position to enable said rotation. Said piston (18) is permanently urged towards its active position by return means (22) and is capable of being displaced towards an inoperative position by fluid supply into a brake release chamber (26). The first and second brake means respectively consist of a first and second series of teeth (16, 20) pertaining to a jaw clutch, the teeth of the first series (16) being integral with the piston (18). The first element (10) and the piston (18) have each a coupling profile (10B, 18B) extending over an axial coupling surface, said coupling profiles forming, viewed in cross-section transverse to the axis of rotation, undulations free from sharp edges, the undulations of the two coupling profiles being capable of fitting into each other to make the piston integral in rotation with the first element.