PURPOSE: To enhance both workability of lathing of a flange section of an outer bearing cylinder and rigidity of the center section of the outer bearing cylinder, by cementing and quenching the outer bearing cylinder after the flange section is integrally incorporated with a substantially center section of outer wall of the outer bearing cylinder upon manufacturing of the outer bearing cylinder.

CONSTITUTION: Upon manufacturing of an outer bearing cylinder 1 for an endlessly sliding ball spline composed of a spline bearing B and a spline shaft which is supported by balls incorporated in the spline bearing, a flange section 2a serving as a flange 2 is integrally incorporated with a substantially center section of outer wall of a thick wall cylinder 1b to form an outer cylindrical element 1c, and thereafter, the thus obtained outer cylindrical element 1c is cemented and quenched. Upon such cementing and quenching differences in wall thickness of the outer bearing cylinder affect strains in the latter, a difference in strain between both end sections and the center section of the outer bearing cylinder comes about so that the inner side of the substantially center section where the flange 2 is formed expands inward, thereby a crowning effect is given to the outer bearing cylinder.