To provide a compact fixed constant velocity universal joint highly efficient with less torque loss and less heat generation which can take a high operating angle and is excellent in the strength and the durability at the high operating angle.

The first track groove part 7a has an arc-shaped ball track central line Xa with a center of curvature without offset to the joint center O in the axial direction. A ball track line central Xb of the second track groove part 7b has a linear portion to increase the effective track length at the maximum operating angle. An end of the ball track central line Xa of the first track groove part 7a is positioned closer to the opening than the joint center O in the axial direction, and the ball track central line Xb of the second track groove part 7b is connected to this end. A ball track central line Y of a track groove 9 of an inner joint member 3 is formed in mirror symmetric to a ball track central line X of a track groove 7 which is paired with an outer joint member 2, in reference to a plane P containing the joint center O in the state of the operating angle of 0°.