This invention is to provide a tappet clearance adjusting cover coupled with a secondary air valve. The tappet clearance adjusting cover is disposed on a cylinder head of an engine. The secondary air valve includes a recessed element and a cap which jointly form a receiving space receiving therein a one-way valve. The recessed element is provided with an inlet pipe interposed between the cap and the tappet clearance adjusting cover. By disposing the secondary air valve on the tappet clearance adjusting cover and arranging the inlet pipe between the cap and the tappet clearance adjusting cover, with the one-way valve received in the receiving space of the secondary air valve, heat dissipation can be improved while the one-way valve is protected against premature deterioration and carbon deposition caused by a high-temperature exhaust gas from the cylinder head. Thus, reliability as well as a service life of the one-way valve is effectively increased.