When an open end spinning machine is stopped, a fiber supply to a spinning rotor is first stopped and thereafter, substantially simultaneously with stoppage of both a yarn take-up roller and a yarn winding roller, a yarn end is held by a yarn holding device at a time when it still remains in a region which undergoes the suction effect of a subatmospheric pressure produced in the spinning rotor. The spinning rotor is subsequently stopped. On starting, the holding of the yarn end by the yarn holding device continues even after restarting of the spinning machine until the subatmospheric pressure produced in the spinning rotor reaches substantially the same value as that produced during a normal spinning operation. Therefore, there is prevented any snarling phenomenon, resulting in a greatly increased success rate in the operation of connecting yarn ends on re-starting of the spinning machine.