Abstract: A pair of header plates securely brazed with a pair of side plates without causing any buckling to tubes and any deformation to the header plates. First, each tube is press-fitted into a corresponding press-fitting hole in the header plates, and at the same time, the end parts of a pair of side plates make contact with the pair of header plates. Second, flaring pins are press fitted into the end parts of the tubes in such a way that the end parts of the tubes disposed near either side of a core assembly are flared to an angle of approximately 180.degree. and the end parts of the tubes disposed in the central part of the core assembly are flared to an angle within a range from approximately 60.degree. to approximately 80.degree.. Third, cores, etc. are hung from either of the upper header plates, whichever is disposed at the upper side, and then this assembly is brazed. At this time, large widening parts with an angle of approximately 180.degree. can prevent the upper header plate from sliding downwards.