PURPOSE: To produce the thin heat exchanger having high strength by increasing the cooling rate after brazing of a brazing sheet formed by using a specifically composed alloy as a core material and cladding an Al alloy brazing filler metal thereon.

CONSTITUTION: The core material of the brazing sheet 1 is composed of the alloy which contains, by weight, 0.4 to 1.2% Si, 0.15 to 1.0% Fe, 0.4 to 1.0% Cu, 0.5 to 1.2% Mn, 0.05 to 0.8% Mg, contains further one or ≥2 kinds of 0.001 to 0.5% Cr, 0. 001 to 0.3% Zr, 0.001 to 1.5% Hf, 0.001 to 0.5% Ti, and 0.0001 to 0.1% B within these ranges, and consists of the balance Al and unavoid able impurities. The heat exchanger is assembled by using the brazing sheet 1 formed by cladding the Al alloy brazing filler metal contg. ≥0.5% Si on one or both surfaces of such core material. After the heat exchanger is heated to and held at the brazing temp., the heat exchanger is cooled at ≥150°C/min cooling rate down to 500 to 200°C.