A universal joint wherein torque-transmitting balls are engaged between complementary grooves formed in an inner and outer joint member, with the balls being supported by a supporting element which is arranged in a jaw-like opening formed on one side of the universal joint through which the balls may be inserted in operative engagement within the joint. The invention is directed toward the curvature of the grooves which are arranged in such a way that a connecting line extending between the center of the radius of curvature of the grooves and the center of the torque-transmitting balls forms an angle relative to the central axis of rotation of the joint which is smaller than or equal to 85.degree., the angle being taken in accordance with the arcsine of the projection of the center of the radius of curvature of the grooves and the ball center onto a vertical plane extending perpendicularly relative to the axis of rotation of the joint, divided by the length of the radius of curvature.