The present invention relates to a method for producing a flat steel product which comprises a base layer composed of a steel material and a multilayer anti-corrosion coating applied thereto, and to a flat steel product, the method comprising the following operating steps: providing the base layer; applying a zinc layer to the base layer by electrolytic coating; applying an at most 25 nm thick aluminum layer to the surface of the zinc layer, the surface of the zinc layer in regard to the oxides and sulfides present thereon being left in the state existing at the end of the electrolytic zinc coating step or occurring during the course of the aluminum coating step as a result of the method; applying a magnesium layer to the aluminum layer; and subsequently heat treating the flat steel product provided with the coating comprising the zinc layer applied to the base layer, the aluminum layer, and the magnesium layer, in such a way that an MgZn2 layer forms in the coating above the Al layer in the direction of the surface of the coating.