PURPOSE: To improve the biting of a rolling mill and to prevent work rolls from producing flaws by providing rolls for processing the tip of strip into a taper shape and a device for traversing the rolls in the width direction of the strip.

CONSTITUTION: A strip 1 is fed in the arrow direction by upper and lower pinch rolls 2a, 2b while being guided by a side guide 3a, and is fixedly held by a clamp 3b after being bitten by rolls 8a, 8b of a rolling mill. Thereafter the tip of strip 1 is roll-formed into a taper shape by traversing a mill housing 7 in the lateral direction of the strip 1 while rotating the rolls 8a, 8b.