PURPOSE: To control an increase in cost of a device by improving the positional and formal accuracies of a curved path to communicate the end of a ball rolling groove to the end of a ball return path corresponding to the above end, and moreover the strength of the end face of a ball spline nut.

CONSTITUTION: An end piece fitting recess 18 where an inner peripheral side is notched larger than an outer peripheral side, and a circumferential space is narrowed on the side of an end is severally provided at positions where a ball rolling groove 12 and a ball return path 15 are opened on both the end faces of a ball spline nut 13. An end piece 17 having an curved path 20 to communicate the end of the ball rolling groove 12 to the end of the ball return path 15 and a projection part fitting in the end piece fitting recess 18 is fitted and fixed in the end piece fitting recess 18.