A coating including polycarbonate-unit-containing polyurethane resin and 5 mass% or more of nonvolatile matter is applied to a traveling metal strip in a state in which the surface temperature of the metal strip is 60°C or lower. Next, the coating applied to the metal strip is baked at 80-250°C, and a coating film having a film thickness of 0.3 µm or greater is formed on the traveling metal strip. The proportion of polycarbonate units to the total mass of resin in the coating film is 10-80 mass%. The traveling metal strip is then wound after being cooling to a surface temperature of 80°C or lower.