A fixed type constant velocity universal joint, comprising: an outer joint member having an inner spherical surface provided with a plurality of track grooves extending in an axial direction, and having an opening side and an inner-end side spaced apart from each other in the axial direction; an inner joint member having an outer spherical surface provided with a plurality of track grooves extending in the axial direction; torque transmitting balls arranged respectively between pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member; and a cage for holding the torque transmitting balls, the cage spherically fitting to both the inner spherical surface of the outer joint member and the outer spherical surface of the inner joint member, wherein all the plurality of track grooves of the outer joint member and all the plurality of track grooves of the inner joint member are each formed into the same shape and the pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member each form a wedge angle (α), the wedge angle (α) comprising a wedge angle (α0) formed, under a state in which an operating angle is 0°, with respect to each of the torque transmitting balls arranged in a joint center plane, and opening to the same side in the axial direction in all the pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member, and wherein the pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member are each formed into a shape which is mirror-image symmetrical with each other with respect to the joint center plane, characterized by the shape of each of the pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member being defined in the axial direction so that, at an operating angle formed by the fixed type constant velocity universal joint, the wedge angle (α) reaches 0° first on the opening side in accordance with movement of the torque transmitting balls to the opening side of the outer joint member, and then, the wedge angle (α) is directed to a direction opposite to a direction in which the wedge angle (α0) opens, and reversely, the wedge angle (α) reaches 0° first on the inner-end side in accordance with movement of the torque transmitting balls to the inner-end side of the outer joint member, and then, the wedge angle (α) is directed to the direction opposite to the direction in which the wedge angle (α0) opens. an outer joint member having an inner spherical surface provided with a plurality of track grooves extending in an axial direction, and having an opening side and an inner-end side spaced apart from each other in the axial direction; an inner joint member having an outer spherical surface provided with a plurality of track grooves extending in the axial direction; torque transmitting balls arranged respectively between pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member; and a cage for holding the torque transmitting balls, the cage spherically fitting to both the inner spherical surface of the outer joint member and the outer spherical surface of the inner joint member, wherein all the plurality of track grooves of the outer joint member and all the plurality of track grooves of the inner joint member are each formed into the same shape and the pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member each form a wedge angle (α), the wedge angle (α) comprising a wedge angle (α0) formed, under a state in which an operating angle is 0°, with respect to each of the torque transmitting balls arranged in a joint center plane, and opening to the same side in the axial direction in all the pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member, and wherein the pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member are each formed into a shape which is mirror-image symmetrical with each other with respect to the joint center plane, characterized by the shape of each of the pairs of the plurality of track grooves of the outer joint member and the plurality of track grooves of the inner joint member being defined in the axial direction so that, at an operating angle formed by the fixed type constant velocity universal joint, the wedge angle (α) reaches 0° first on the opening side in accordance with movement of the torque transmitting balls to the opening side of the outer joint member, and then, the wedge angle (α) is directed to a direction opposite to a direction in which the wedge angle (α0) opens, and reversely, the wedge angle (α) reaches 0° first on the inner-end side in accordance with movement of the torque transmitting balls to the inner-end side of the outer joint member, and then, the wedge angle (α) is directed to the direction opposite to the direction in which the wedge angle (α0) opens.