The oxide film thickness of the steel material surface (d H2O +d o2 ) is made to become 15 nm or less where post-treatment after water-cooling is not needed by suitably setting the conditions of the water-cooling start temperature (T i ), water-cooling end temperature (T o ), steel material thickness (d), concentration of solute oxygen in the cooling water (D o ), and cooling rate (C R ) in the equation of d H2O +d o2 ="7".98&dlowbar;10 -4 (T i -T o ) dD o +{5.50&dlowbar;10 -3 (T i 2 -T o 2 )-6.51 (T i -T o )}/C R .