PURPOSE: To make improvement in brazing characteristic by specifying the contents of Mg in a core material and sheath material constituting the brazing sheet.

CONSTITUTION: The contents of the Mg in the core material and sheath material constituting the brazing sheet which is constituted by forming the sheath material consisting of the Al alloy having the m. p. lower than the m. p. of the core material on at least one surface of the Al alloy core material and executing brazing in a nonoxidative atmosphere by using a non-corrosive fluoride flux are specified to ≤0.03wt.%. The good brazed joint is obtd. with a small amt. of flux in this way and this method is particularly effective in the case of production of the evaporator of the lamination type having the joint part particularly in a heat exchanger.