Method for the manufacture of a flat steel product coated with a corrosion protection system, in which a first metallic layer is applied onto a steel substrate forming the base layer of the flat steel product and a second metallic layer is applied onto the first metallic layer, which, as a consequence of heat treatment, becomes an alloy with the first metallic layer, wherein the total thickness of a metallic coating formed from the first and second metallic layers amounts to less than 3.5 μm, in which a plasma polymer layer is applied onto the metallic coating formed from the first and second metallic layers.