A constant velocity universal joint comprises an outer joint element having a spherical cavity therein and an inner joint element positioned within the spherical cavity. A plurality of torque transmitting balls are positioned within pairs of opposed grooves formed in the opposing spherical surfaces of the inner and outer joint elements. Ball retaining means are disposed between the joint elements. The ball retaining means has an inner spherical surface co-acting with the outer spherical surface of the inner joint member and an outer spherical surface co-acting with the spherical surface of the cavity of the outer joint element. The number of grooves in each joint element is divisible by two but is at least four and the center line of each groove lies in a plane spaced from the axis of rotation of the joint element and parallel thereto.