cooling tank 1 and the water in the tank 1 is overflowed through a discharge pipe 6 to be recovered as hot water it will be described a typical example of the invention referring to the embodiment shown in fig4 a steel strip having a thickness of 0 5 to 1 5 mm and a width of 900 to 1 400 mm was finally cooled by injecting cooling water jets from the injection nozzles arranged in the cooling water the temperature of the cooling water tw was controlled at 80 u00b0 c and the length of the steel strip subjected to the cooling water jets l was 1 2 meters the speed of steel strip v 60 m min multiplied by the strip thickness d u00d7 10 3 mm was controlled to two hundred and fifty the temperature of the steel strip was reduced through the cooling zone 16 from 350 u00b0 c to 270 u00b0 c at the inlet of the cooling tank as a result of a macroscopic test there was no dirt on the surface of the steel strip after final cooling while for the purpose of comparing the steel strip was cooled by a conventional immersing manner under the same condition as the above fig7 is a graph showing the dead zones of dirt adhesion according to the present invention and the conventional manner obtained as a result of the above comparing tests it was found from the comparing tests that in order to prevent the dirts from adhering to the surface of the strip.