The oxide film thickness of the steel material surface (dH2O+do2) 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 (Ti), water-cooling end temperature (To), steel material thickness (d), concentration of solute oxygen in the cooling water (Do), and cooling rate (CR) in the equation of dH2O+do2=7.98×10−4(Ti−To)dDo+{5.50×10−3(Ti2−To2)−6.51(Ti−To)}/CR.