atmosphere to remove free si contained in the composite thereby preparing a ceramic matrix composite according to example 2 the matrix of the composite according to example 2 consisted of sic and mosi 2 and had a density ratio of 90 or more a ceramic matrix composite prepared in example 1 was heated a temperature of 1 300 to 1 400 u00b0 c in a nitrogen pressed atmosphere to nitrify free si on the surface of the composite material and near the surface and to form a surface layer containing silicon nitride si 3 n 4 thereby preparing a ceramic matrix composite according to example 3 the internal structure of the matrix of the composite according to example 3 consisted of sic mosi 2 and free si and a surface layer having a composition of sic mosi 2 si 3 n 4 was formed on the surface and near the surface of the composite a ceramic matrix composite prepared in example 1 was heated to a temperature of 1 300 to 1 400 u00b0 c in a nitrogen atmosphere to ooze free si left in the composite to the surface portion of the composite and the oozed free si on the surface portion was nitrified to form a surface layer containing silicon nitride si 3 n 4 thereby preparing a ceramic matrix composite according to example 4 the internal structure of the matrix of the composite according to example 4 consisted of sic and mosi 2 and a surface layer having a composition.