Abstract: In brazing a first metal piece having a tubular joint portion of predetermined length at an end thereof and a second metal piece having a bore for inserting the extremity of the joint portion thereinto by replaced brazing with the extremity of the joint portion inserted in the bore, a plurality of axial grooves having a depth of 0,3 to 1,5 mm and arranged at a spacing of 5 to 30 mm in the circumferential direction are formed in the outer peripheral surface of joint portion of the first metal piece. Each of the grooves has one end extending to the outside of the bore of the second metal piece when the joint portion is inserted in the bore. The gas or residue of flux produced during brazing escapes through the grooves, whereby voids or like defects are prevented from occurring in the fillet of the brazed joint. Since the grooves are all filled up with the brazing filler metal, the brazed joint is given a sufficient bond strength and prevented from permitting leakage there-through.