The invention relates to a method for producing improved cold-rolled band that is capable of being deep-drawn or ironed and that has a carbon content of less than 0.5 weight %. The invention also relates to a cold-rolled band that can be produced by such a method, and preferably used for producing cylindrical containers and, in particular, battery containers by deep-drawing or ironing. The band that is cold-rolled with a cold-rolling ratio ranging from 30 to 95% is subjected to a thermal treatment in an annealing furnace and to a—preferably galvanic—coating of at least one of the two band surfaces. In order to obtain an isotropic steel band that has a low level of texturing and that has a low tendency to form earing, the coating produced with one or multiple layers contains the elements of nickel/cobalt/iron/bismuth/indium/palladium/gold/tin, or alloys thereof, where the thermal treatment is effected by annealing, which is carried out—before or after the coating process—in a continuously running band-annealing furnace at a temperature greater than the limit temperature of the austenite range ( range).