An engine starter motor comprising an electric motor, a unidirectional clutch connected to the motor and having an output shaft, the unidirectional clutch exhibiting a drag torque appearing when the unidirectional clutch is being rotated in an idle direction, a speed reduction unit connected to the unidirectional clutch, and a pinion shaft having a pinion gear for engaging and driving an engine ring gear and connected to the speed reduction unit through helical splines. The drag torque T of the unidirectional clutch is determined to be equal to or smaller than a drag torque To, at which a return force F on the pinion shaft with an over-running clutch mounted thereon does not exceed an operating force on the pinion shaft by a solenoid, divided by a speed reduction ratio g between the over-running clutch and the pinion shaft.