A strip member is wound by a tire building machine having a building drum for taking up a strip member of predetermined length without discrete ends and a transfer conveyor for feeding the strip member to the building drum. The winding-start end of the strip member transferred from the transfer conveyor to the building drum and the winding-finish end of the strip member are detected by means of end sensors, measuring the angle through which the building drum has rotated from the output of a winding start signal to the output of a winding finish signal in response to output signals from the sensors by means of an angle detector. A lapping margin between the winding start end and the winding finish end of the strip member is calculated based on the rotational angle and diameter of the building drum by means of an operational means.