A non-oxide ceramic material such as aluminum nitride can be metallized with copper by directly bonding a thin sheet of copper to a substrate of the non-oxide ceramic material instead of using a conventional manner in which a paste comprising a powder of copper and a binder is applied to a ceramic substrate by printing. This metallization is effected by placing the non-oxide ceramic material either in contact with or in close proximity to copper containing a copper oxide, followed by heating them in a non-oxidizing atmosphere at a temperature lower than the melting point of copper, but at which the dissociation of the copper oxide contained in copper can occur, so as to dissociate at least part of the copper oxide into metallic copper and oxygen to thereby provide a strong bondage between the surfaces of said non-oxide ceramic material and copper. The metallized non-oxide ceramic material can be used as a substrate for use in IC devices.