PURPOSE: To improve galling resistance, chemical convertibility and spot weldability by selecting an atmosphere contg. prescribed components and carrying out cooling under prescribed conditions when a cold rolled steel sheet is continuously annealed in an annealing furnace.

CONSTITUTION: A cold rolled steel sheet contg. ≤0.01wt.% C and ≤0.01wt.% N is continuously annealed in an annealing furnace having heating, soaking and cooling zones. In the latter stage of soaking or the early stage of cooling in the annealing furnace, the steel sheet is exposed to a carburizing or carbonitriding atmosphere to form a layer contg. thickened C and N in the surface of the steel sheet and the steel sheet is immediately cooled to 500°C at ≥10°C/sec average cooling rate.