A fixed type constant velocity universal joint has cutout round portions (32) provided at two portions of a ball-contact-point corresponding part on a track inlet end (22a) of each of the track grooves (22) of the outer joint member for reduce biting of balls. The fixed type constant velocity universal joint is capable of achieving reduction of stress generated when balls and edge portions interfere with each other, suppression of chipping of the edge portions, and prolongation of a service life of the joint as a whole. These advantages are achieved even at a time of an unexpected high-angle operation, and in particular even when an angle expected during use of the constant velocity universal joint is exceeded.