A fixed type constant velocity universal joint of a track groove crossing type has track grooves of an inner joint member formed to be mirror-image symmetrical with paired track grooves of an outer joint member with respect to a joint center plane at an operating angle of 0°. The track grooves of both the joint members each have a length corresponding to a maximum operating angle (θmax) required for a propeller shaft, and surface treatment is performed, for example, on a defined surface of each of the track grooves of the outer joint member so as to reduce frictional resistance (sliding resistance) against balls.