PURPOSE: To prevent a material to be heat-treated from being discolored in the cooling step, by cooling it with cooling water containing an additive, in a cooling tank provided in a reducing atmosphere, in case of using said atmosphere.

CONSTITUTION: In a bright continuous annealing furnace using a reducing atmosphere, a material to be heat-treated is water-cooled in a cooling tank provided in the reducing atmosphere. Cooling water is stored in a storage tank after adding benzotriazole, and it is fed to the cooling tank by a pump. The cooling water which has ended cooling overflows, passes through a U-pipe to be gas- sealed, and returns to the storage tank through a drain pipe. To this cooling water, benzotriazole has been added, therefore, its surface tension is small, and large drops of air-bubbles are generated. Accordingly, the air-bubbles generated on the surface of the material to be heat-treated float up from the surface immediately, and its discoloration caused by air-bubbles is prevented.