A heat exchanger core assembly having an improved tube-to-header joint construction wherein each individual tube end portion is preformed into a diamond-shaped configuration and each mating header plate is likewise preformed to include a plurality of diamond-shaped openings adaptable for receiving the corresponding diamond-shaped tube ends therethrough. Each tube member includes a body portion, a diamond-shaped end portion located at each opposite end thereof, and a gradual transition section which extends from each opposite end of the tube body portion to the respective diamond-shaped tube end portions. When mated together, each tube-to-header joint is bonded together such as by soldering or brazing. Each of the diamond-shaped openings in the mating header plates may also include an increased flange area extending at least partially therearound to improve the structural integrity and strength of the soldered or brazed joint between the tube end portions and the mating header plates.