A paste of active metallic brazing material is applied to the entire surface of each side of aluminum nitride or alumina ceramic substrate 1; circuit forming copper plate 3 having a thickness of 0.3 mm is placed in contact with one surface of the substrate and a heat dissipating copper plate 4 having a thickness of 0.25 mm placed in contact with the other surface; the individual members are compressed together and heated at 850.degree. C. in a vacuum furnace to form a joint; an etching resist is applied to the circuit forming copper plate and etching is performed with an iron chloride solution to form a circuit pattern and the unwanted brazing material is removed from the marginal portions; a second resist layer is applied and etched with an iron chloride solution to form a second marginal step; a third resist layer is similarly applied and etched to form a third marginal step; the completed circuit board having three marginal steps of which the lowest one is solely or partly made of the brazing material can withstand 1,500 heat cycles, which is the result that has ben unattainable by the prior art. Having such high heat cycle characteristics, the circuit board is suitable for use as semiconductor substrate in automobiles, electric trains and other applications that require high output power.