PURPOSE: To finish an outer race with a min. of the deformation by a heat treatment and uniformity, by immersing the outer race together with a bottomed cylindrical part of the specific shape enclosing the outside part thereof in liquid and heat treating the same.

CONSTITUTION: A bottomed cylindrical part 3 is positioned to the outer race 2 of a constant velocity ball joint 1 consisting of a cup 1a and a shaft 1b in one body so as to enclose the race 2 coaxially. The part 3 is formed to such a shape in which the top end surface of the part 3 is higher than the bottom surface of the race 2 and that the volume of the space 4 formed of the inside circumferential surface 3a and bottom surface 3b thereof and the contour of the race 2 is equal to the inside volume of the cup 1a. When the two parts which are set in the above-mentioned way are immersed in the cooling liquid, the liquid flows to the inside and outside circumferences of the race 2 as shown by arrows A, B. Since the space 4 and the race 2 have the same inside volume, the cooling rates on the inside and outside circumferences of the race 2 are equal.