PURPOSE: To omit an escape working process and to shorten the process, by forming a polishing escape of a ball rolling groove of a uniform universal joint outer ring simultaneously together with the ball rolling groove by means of plastic working.

CONSTITUTION: A core surface 2, a core surface 3 and a core surface 4 form a ball rolling surface 2' of a uniform universal joint, a polishing escape part 3' of the grooved bottom part of the universal joint, and a polishing escape part 4' of both corner parts of the groove of the universal joint, respectively. In this way, not only working of the groove part is performed but also the polishing escape is provided on a coarse shape material, therefore, it is unnecessary to add a process for working the escape, and the process is shortened.