According to this invention, a spinning rotor is increased in speed until it reaches a predetermined higher speed beyond a lower speed region and then decreased in speed until it falls within the lower speed region, in which a yarn ending is effected. Thereafter, the speed of the spinning rotor is increased to a normal spinning speed beyond the predetermined higher speed. During rotation of the spinning rotor at the predetermined higher speed, sufficient subatmospheric pressure is produced in the spinning rotor to stretch out the yarn end thereby to prevent the yarn end from being snarled. Also, during this higher speed rotation of the spinning rotor, sufficient fibers in the spinning rotor can be collected in a maximum diameter portion in the spinning rotor to be connected with the snarl-free yarn end in a favorable condition. The period of time, during which the speed of the spinning rotor is decreased from the predetermined higher speed and falls within the lower speed region, is relatively short being in the order of a few or several seconds. Therefore, it will be understood that there is no fear that both the yarn end and the remaining fibers are restored to their initial state during that period of time.