PURPOSE: To prevent the generation of an edge crack in cold rolling and to improve the yield of a cold rolled product by heating the edge part of a steel strip to a prescribed temp. or above prior to cold rolling of the steel strip and making the hardness over the entire part of the strip including the edge part uniform.

CONSTITUTION: A steel strip 1 after hot rolling is unwound with an un-coiler 3, and after the defective end part is cut away 4, the preceding steel strip and the succeeding steel strip are welded and connected by a welder 5. The strip 1 after the connection is passed through an inlet side loop car 6 and a bridle roll 7 in a continuous descaling device 8 and is removed of surface scale during this time. The strip 1 subjected to a pickling treatment 9 is fed through a bridle roll 12 and an outlet side loop car 13 to a side trimmer 14 where the edge part of the strip 1 is side trimmed and thereafter the edge part is annealed by heating to a desired temp. of ≥400°C. Such strip 1 is passed through a tension bridle roll 16 and in succession, it is coated 17 thereon with a rust preventive oil and is cut 18 for every specified length. After the cut strip is coiled by each specified length on a tension reel 19, the coil is transferred to a cold rolling installation and is thereby cold rolled.