A composite laminate, including shrink-prevention ceramic green sheets arranged on the main surfaces of an unfired ceramic laminate and having a sintering temperature greater than the firing temperature of the unfired ceramic laminate, is fired at a temperature which is greater than the sintering temperature of the unfired ceramic laminate, and which is less than the sintering temperature of the shrink-prevention ceramic green sheet. Thereafter, the shrink-prevention ceramic green sheets are removed in a first removing step of spraying water and compressed gas against the shrink-prevention ceramic green sheets so as to remove a portion thereof that has not reacted with a glass component of the unfired ceramic laminate, and in a second removing step of ceramic powder, spraying water, and compressed air, such that a residual material not removed in the first removing step is removed, and in a third removing step of supersonic-cleaning the ceramic multi-layer substrate after the first and second steps.