A rear suspension for a vehicle such as a bicycle or motorcycle that includes a frame, a swinging arm integral with the frame carrying the axle of a drive wheel hub and a shock absorber whose ends are secured to the frame and to the swinging arm, the swinging arm being secured to said frame by at least two articulation means so that the swinging arm pivots about an "instantaneous centre of rotation" that is movable when the hub is displaced on either side of its reference position corresponding to the position of the hub axle when the vehicle is in a static equilibrium position, characterized in that the instantaneous centre of rotation is displaced upwards along a parabolic path, the asymptote of which is oriented towards the rear free end of the swinging arm carrying the axle of the hub when said hub is displaced above its reference position.