A four-cycle engine is provided that includes an exhaust port for releasing combusted gas from the engine and an exhaust system. The exhaust system includes an exhaust pipe coupled with the exhaust port, a first catalyst, a second catalyst, and a secondary air introduction pipe. The first catalyst is disposed in the exhaust pipe and the second catalyst is disposed in the exhaust pipe a set distance downstream of the first catalyst. The secondary air introduction pipe is configured to introduce air into the exhaust pipe. The secondary air induction pipe is connected to the exhaust pipe between the first and the second catalysts at a location where a temperature difference of the first and the second catalysts in a cold start transient phase is within a predetermined range.