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PROBLEM TO BE SOLVED : To provide a method simply enabling to reduce S concentration and N concentration in a steel by injecting desulfurizing agent for short time with a uniprocess using an RH type vacuum-degassing apparatus.SOLUTION : When the desulfurization and the denitorogenization are performed by injecting desulfurizing agent on the molten steel composed by mass% of 0.005-1.0% Al concentration, ≤0.003% S concentration, ≤0.003% O concentration and ≤0.005% N concentration from a top-blowing lance set in a vacuum vessel in the RH type vacuum-degassing apparatus, this method for desulfurizing and denitrogenizing the molten steel at high speed, particularly uses the one as the desulfurizing agent, in which massive mixing ratio of the rare-earth metals (REM) and (CaO), (REM)/(CaO), satisfies the following formula (1) : (1) 0.02≤(REM)/(CaO)≤0.3.