The outer peripheral surface (32) and the inner spherical peripheral surface (34) of a cage (30) of a double-offset constant velocity universal joint are cut after being quenched. More specifically, to finish the outer peripheral surface (32) of the cage (30) made up of a spherical portion (32a) and tapered portions (32b, 32c), the spherical portion (32a) and the tapered portions (32b, 32c) are cut after being quenched. Then, the spherical portion (32a) is cut at a cutting speed lower than that for the tapered portions (32b, 32c), thereby providing a better roughness to the cut surface of the spherical portion (32a) than to the cut surface of the tapered portions (32b, 32c).