A method for joining a ring member, e.g. a bearing inner race ring, to a shaft so that the ring member is primarily prevented from axial motion relative to the shaft involves arranging the ring member over the shaft so that the shaft extends through a bore in the ring member, and applying between the ring member and the shaft a clamping wedge force in which a tapering locking surface acts against a substantially corresponding tapering surface. The device for joining the ring member to the shaft includes a locking member mounted on the ring member and provided with a tapering contact surface that faces towards the shaft. An arrangement is provided for pressing the locking element against a tapering counter surface that is fixed in position relative to the shaft to prevent axial movement of the ring member on the shaft.