In manufacture of a heat exchanger, heat exchange tubes, fins, and header section bodies are arrange in an assembled condition. Projection pieces provided on caps of header sections are fitted into corresponding slits formed in side plates, thereby engaging end portions of the side plates with the caps. In this condition, the caps are arranged in such a manner as to bridge end portions of the header section bodies, and the side plates are arranged on the outer sides of the leftmost and rightmost fins. The heat exchange tubes and the fins, the heat exchange tubes and the header section bodies, the header section bodies and the caps, the side plates and the caps, and the side plates and the fins are respectively brazed together simultaneously. This method enables the side plates to be accurately arranged at respectively predetermined positions.