A novel brake assembly is provided for a bicycle. The assembly is composed of an arrangement of a pair of brake pads each connected to a rod member in turn guided for axial movement by a base fixed on the bicycle frame. A bifurcated control cable actuates wedge members causing movement of the pads against a wheel rim. Return springs on the rod members cause the assembly to return to the original non-braking position in response to release of the control cable. As an option, a second wedge action can be incorporated that is activated by the frictional forces generated from the contact of the brake pads with the wheel rim. The second wedge action is limited by a mechanical stop within the brake assembly to prevent jamming of the brakes.