A method of manufacturing a flat steel product coated with a corrosion protection system, in which a zinc-based coating is applied to a steel substrate, such as a steel strip or sheet, by hot dip coating, and in which an organic coating is applied to the zinc-based coating, comprising the following steps: - preheating the steel substrate in a preheating furnace to a strip temperature of 720 - 850 °C under a protective gas atmosphere; - cooling the steel substrate to a strip entry temperature - hot dip coating of the steel substrate hermetically sealed in a zinc bath, which contains, in addition to zinc and unavoidable impurities (in wt.%), 0.15 - 0.4 % Al, 0.2 - 3% Mg and optionally in total up to 0.8 % of one or more elements of the group "Pb, Bi, Cd, Ti, B, Si, Cu, Ni, Co, Cr, Mn, Sn and rare earths" and whose bath temperature is 420 - 500 °C, - whereby the difference "BET-BT" between the strip entry temperature "BET" and the bath temperature "BT" is varied in the range of -10 °C to +70 °C in such a manner that a metallic Zn-Mg-Al-Fe-containing corrosion protective coating is formed on the steel substrate, which contains (in wt.%) 0.25 - 2.5 % Mg, 0.2 - 3.0 % Al, ≤ 4.0 % Fe, and optionally in total up to 0.8 % of one or more elements of the group "Pb, Bi, Cd, Ti, B, Si, Cu, Ni, Co, Cr, Mn, Sn and rare earths", remainder zinc and unavoidable impurities and which has, in an intermediate layer extending between a surface layer immediately adjacent to the surface of the flat steel product and a boundary layer adjacent to the steel substrate, and whose thickness is at least 20% of the total thickness of the corrosion layer coating, an A1 content of at most 0.5 wt.%, - adjusting the thickness of the metallic corrosion protective coating applied to the steel substrate in the molten bath to values of 4 - 12 μm - corresponding to a layer weight of 30 - 85 g/m 2 - on each side by stripping excess coating material - cooling the steel substrate provided with the metallic corrosion protective coating and - applying the organic coating to the metallic corrosion protective coating of the steel substrate. - preheating the steel substrate in a preheating furnace to a strip temperature of 720 - 850 °C under a protective gas atmosphere; - cooling the steel substrate to a strip entry temperature - hot dip coating of the steel substrate hermetically sealed in a zinc bath, which contains, in addition to zinc and unavoidable impurities (in wt.%), 0.15 - 0.4 % Al, 0.2 - 3% Mg and optionally in total up to 0.8 % of one or more elements of the group "Pb, Bi, Cd, Ti, B, Si, Cu, Ni, Co, Cr, Mn, Sn and rare earths" and whose bath temperature is 420 - 500 °C, - whereby the difference "BET-BT" between the strip entry temperature "BET" and the bath temperature "BT" is varied in the range of -10 °C to +70 °C in such a manner that a metallic Zn-Mg-Al-Fe-containing corrosion protective coating is formed on the steel substrate, which contains (in wt.%) 0.25 - 2.5 % Mg, 0.2 - 3.0 % Al, ≤ 4.0 % Fe, and optionally in total up to 0.8 % of one or more elements of the group "Pb, Bi, Cd, Ti, B, Si, Cu, Ni, Co, Cr, Mn, Sn and rare earths", remainder zinc and unavoidable impurities and which has, in an intermediate layer extending between a surface layer immediately adjacent to the surface of the flat steel product and a boundary layer adjacent to the steel substrate, and whose thickness is at least 20% of the total thickness of the corrosion layer coating, an A1 content of at most 0.5 wt.%, - adjusting the thickness of the metallic corrosion protective coating applied to the steel substrate in the molten bath to values of 4 - 12 μm - corresponding to a layer weight of 30 - 85 g/m 2 - on each side by stripping excess coating material - corresponding to a layer weight of 30 - 85 g/m 2 - on each side by stripping excess coating material - cooling the steel substrate provided with the metallic corrosion protective coating and - applying the organic coating to the metallic corrosion protective coating of the steel substrate.