a method for mounting an axially split sleeve provided with an axial slot on a shaft so that a tapering surface on the sleeve cooperates with a tapering bore of a machine member . a flange is axially connected to the sleeve and supports a number of spaced apart tightening devices that are to be urged against the machine member for mutually displacing the machine member and the sleeve to increase the grip between the shaft , the sleeve and the machine member . the method involves positioning the sleeve around the shaft with the annular flange positioned with its tightening devices against the machine member , tightening a first one of the tightening devices which is located at a position diametrically opposite the slot in the sleeve , and thereafter tightening further ones of the tightening devices one by one .