A fixed type constant velocity universal joint, comprising: an outer joint member having a spherical inner peripheral surface in which a plurality of track grooves are formed so as to extend in an axial direction of the outer joint member; an inner joint member having a spherical outer peripheral surface in which a plurality of track grooves are formed so as to be paired with the plurality of track grooves of the outer joint member; balls for transmitting torque, the balls being interposed between the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member, which are paired with each other; and a cage comprising pocket portions for receiving the balls, the cage having: a spherical outer peripheral surface fitted to the spherical inner peripheral surface of the outer joint member; and a spherical inner peripheral surface fitted to the spherical outer peripheral surface of the inner joint member, wherein the plurality of track grooves of the outer joint member are each formed into an arc shape having a curvature center that is prevented from being offset in the axial direction with respect to the joint center, the plurality of track grooves of the outer joint member being inclined in a peripheral direction of the outer joint member with respect to the joint axial line (N-N) and being adjacent to each other in the peripheral direction with their inclination directions opposite to each other, wherein the plurality of track grooves of the inner joint member are formed so as to be mirror-image symmetrical with the plurality of paired track grooves of the outer joint member with respect to a joint center plane at an operating angle of 0°, wherein the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member each have a length corresponding to a maximum operating angle (θ max) required for a propeller shaft, characterized in that the fixed type constant velocity universal joint is subjected to surface treatment in at least the spherical inner peripheral surface of the outer joint member, the spherical outer peripheral surface of the inner joint member, the spherical outer peripheral surface of the cage and the spherical inner peripheral surface of the cage, the surface treatment being performed so as to reduce frictional resistance of the surfaces (6, 8, 12, 13) against a mating member that relatively moves in contact with the surfaces (6, 8, 12, 13). an outer joint member having a spherical inner peripheral surface in which a plurality of track grooves are formed so as to extend in an axial direction of the outer joint member; an inner joint member having a spherical outer peripheral surface in which a plurality of track grooves are formed so as to be paired with the plurality of track grooves of the outer joint member; balls for transmitting torque, the balls being interposed between the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member, which are paired with each other; and a cage comprising pocket portions for receiving the balls, the cage having: a spherical outer peripheral surface fitted to the spherical inner peripheral surface of the outer joint member; and a spherical inner peripheral surface fitted to the spherical outer peripheral surface of the inner joint member, a spherical outer peripheral surface fitted to the spherical inner peripheral surface of the outer joint member; and a spherical inner peripheral surface fitted to the spherical outer peripheral surface of the inner joint member, wherein the plurality of track grooves of the outer joint member are each formed into an arc shape having a curvature center that is prevented from being offset in the axial direction with respect to the joint center, the plurality of track grooves of the outer joint member being inclined in a peripheral direction of the outer joint member with respect to the joint axial line (N-N) and being adjacent to each other in the peripheral direction with their inclination directions opposite to each other, wherein the plurality of track grooves of the inner joint member are formed so as to be mirror-image symmetrical with the plurality of paired track grooves of the outer joint member with respect to a joint center plane at an operating angle of 0°, wherein the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member each have a length corresponding to a maximum operating angle (θ max) required for a propeller shaft, characterized in that the fixed type constant velocity universal joint is subjected to surface treatment in at least the spherical inner peripheral surface of the outer joint member, the spherical outer peripheral surface of the inner joint member, the spherical outer peripheral surface of the cage and the spherical inner peripheral surface of the cage, the surface treatment being performed so as to reduce frictional resistance of the surfaces (6, 8, 12, 13) against a mating member that relatively moves in contact with the surfaces (6, 8, 12, 13).