Abstract: An antibacklash splined shaft (14) is formed by first machining splines (22) in the end of the shaft, thereafter forming an axial bore (26) in the shaft, and thereafter forming slots (28) in the shaft that extend from between the spline into the bore. When the slots are formed, the teeth flex slightly outwardly to relieve the internal stresses in the shaft. Thus, when the splined shaft (14) is inserted into an internally splined member, the teeth are biased outwardly so as to firmly and intimately engage the internal splines, providing a coupling that exhibits no backlash.