By the use of a heat exchanger tube not required for adhesion of Zn in advance and a fin not clad with a brazing composition, a heat exchanger core is provided which has corrosion resistance and brazing capability comparable to or higher than those of the conventional counterpart. Applied onto an outer surface of an extruded flattened tube as a heat exchanger tube is a brazing composition derived from a mixture of silicon and fluorine type flux, and a fin formed of an aluminum-based zinc-containing material is prepared. The extruded flattened tube and the fin are then heated at a given temperature so that the same are brought into brazed relation to each other, and a mixed diffusion layer of silicon and zinc is then on the outer surface of the extruded flattened tube.