A rolled metal strip which is free of torsion and on which a superior gloss is obtained by a combination of cross rolling and parallel rolling upon cold rolling a metal strip and by rolling the material in a parallel rolling manner in either at least the final stand (in the case of a tandem mill array) or at least the final pass (in the case of a single stand mill such as a reversible mill or the like). If necessary, the metal strip is preliminarily rolled by cross rolling at a rolling reduction rate of over 5% and then cold rolled by either parallel rolling or a combination of cross rolling and parallel rolling.