A 4-cycle engine for a motorcycle has a secondary-air supplier for supplying secondary air to exhaust ducts. The engine includes a recess, which is depressed toward the engine, on a cylinder-head cover for holding a control valve of the secondary-air supplier. The recess and the control valve are positioned between two innermost cylinders of the array of the cylinders. Check valves, which are connected to downstream regions of the control valve, are each disposed between two outermost cylinders of the array of the cylinders.