A fixed constant velocity universal joint includes an outer race having a spherical inner circumferential surface, the outer race including axially extending ball grooves formed in the spherical inner circumferential surface at regular circumferential intervals, and an inner race having a spherical outer circumferential surface, the inner race including axially extending ball grooves formed in the spherical outer circumferential surface at regular circumferential intervals. Balls are interposed between pairs of the ball grooves of the outer race and the ball grooves of the inner race. A cage has pockets for receiving the balls, the pockets being formed at predetermined circumferential intervals. The outer race is produced by hot forging or lathe-turning and subjected to thermal refining treatment.