PURPOSE: To roll a connection material without rolling it up with a cold tandem consecutive mill by controlling a load so that it is fixed through the last stand or both the last stand and the stand before the last stand.

CONSTITUTION: A material suitable in deformation resistance, width, thickness is selected as the connecting stock 3 between the last stock 1 of the previous cycle and a base stock 2 of the present cycle. The plate thickness on the outlet side of the last stand is measured to control a load given to a roll, a rotational speed of one stand before the last stand is controlled to control the tension and the load is controlled so that it is fixed. In this way, generation of roll edge marks on the surface of the material is reduced and the connected part of the coil is passed without opening the roll gap.