A system and method for reducing non-repeatable positioning errors. Non-repeatable positioning errors caused by the effects stiction and backlash in the mechanical system are reduced by "shaking" or vibrating the positioning system in a controlled manner. After the system input is set to the desired value, the positioning system is "shaken" by inputting a series of offsets that oscillate around the desired location and gradually decrease in amplitude, eventually reaching zero. In a specific embodiment, a lead screw is threaded through a follower nut which is connected to a magnetic tape read/write head. The lead screw is rotated by a mechanical transmission which provides gear reduction from a computer controlled stepper motor. The tape head's non-repeatable positioning error is reduced by alternately stepping the stepper motor in opposite directions a specified number of steps and periodically reducing the specified number of steps until zero is eventually reached.