A method by which a flat steel product containing 2-35 wt. % of Mn can be provided with a coating of Zn which adheres well by annealing at an annealing temperature Ta of 600-1100° C. for an annealing time of 10-240 s under an annealing atmosphere which has a reducing effect on the FeO present on the flat steel product and an oxidizing effect on the Mn contained in the steel substrate thereby forming a layer of Mn mixed oxide which covers the flat steel product at least in sections and then cooling the flat steel product to a temperature for bath entry and conveying it through a bath of molten Zn saturated within iron at a temperature of 420-520° C., within a dip time of 0.1-10 s.