PURPOSE: To check defective tearing from developing at the end of a thickness- deviated rolling material during the cold rolling by chamferring the vertical face of a thick side end thereof in a tapered shape beforehand.

CONSTITUTION: Either or both of the vertical face of a thick side end of a thickness-deviated rolling material is chamferred at an obtuse angle in a tapered shape with respect to the vertical face of the end thereof prior to the cold rolling. For example, a thickness-deviated rolling material 2 is guided to an end grinding mechanism. There, it is moved fixed with a press roller 4 and chamferred at both s are corners of the thick side end E1 with a thick side end grinding tool 9 properly adjusting thereof. The pretreatment makes possible a good rolling without tearing at the end of the material during the rolling.