a transmission for a bicycle includes a derailleur shaft supported by a case member . a derailleur arm is movably journaled by the derailleur shaft . a guide rotational body is rotatably supported by the derailleur arm and an endless power transmission belt is wound therearound . the endless power transmission belt is shifted among a plurality of rotational body elements which constitute a speed - change rotational body for changing the speed - change ratio . an operating pin is connected to a wire which moves in the fore - and - aft direction in accordance with the speed - change operation so that the derailleur arm is rotated with respect to the derailleur shaft and translated toward the center axis of the derailleur shaft by the operating pin being moved while being guided through the guide hole by the speed - change operation via the wire . a roller is rotatably journaled by the operating pin is rotatably fitted in the guide hole .