To obtain a stable fluxless joining state in brazing in a non-oxidizing atmosphere under an atmospheric pressure.

The stable joining state is achieved by a fluxless brazing method using a brazing sheet located at the uppermost surface and obtained by cladding a brazing material containing 5.0 to 12.0 mass% of Si and 1.0 to 5.0 mass% of Mg and having a liquidus temperature of 610°C or less to a core material, in which the brazing material and a member to be brazed are caused to come into close contact, and brazing thermal processing is performed in a non-oxidizing atmosphere including an oxygen concentration of 50 ppm or less while keeping the brazing heating temperature at 590°C or more for three minutes or more, and the core material and the member to be brazed are joined at the closely-contacted surface of the close contact part by the brazing material.