A constant velocity universal joint has high strength and capable of suppressing deformation caused by quenching at an opening end portion of a track groove of an outer joint member. In an undercut-free constant velocity universal joint in which a track groove in a cup portion of the outer joint member has a hardened layer formed by induction quenching, an opening end surface is protruded by a protruding amount t in an axial direction from a groove bottom of the track groove in a relief surface. The protruding amount t satisfies a relation of t=0.037d to 0.185d when a diameter of a torque transmission ball is represented by d. The opening end surface in a protruded portion and an outer surface of the cup portion continuous to the opening end surface have an unhardened layer free from hardening by quenching.