A bicycle disc brake is provided in which a support member movably couples the brake caliper to the frame of the bicycle. The bicycle disc brake caliper has a caliper housing with a single piston unit. The piston unit is movably coupled to the housing between a release position, in which the piston unit is spaced from a disc brake mounted to a wheel of a bicycle, and a braking position, in which the piston unit engages the disc brake of the bicycle wheel. The piston unit has a first friction member movably coupled between a release position and a braking position and a second friction member arranged substantially parallel to the first friction member to form a disc brake receiving space between the first and second friction members. In one embodiment, the caliper housing is movably coupled to the support member by a pivot pin. In another embodiment, the caliper housing is movably coupled to the support member by a linkage assembly.