Method for hot-dip coating a flat steel product, consisting of (in % wt.) C: ≤1.6 %, Mn: 2 - 35 %, Al: ≤ 10 %, Ni: ≤ 10 %, Cr: ≤10 %, Si: ≤ 10 %, Cu: ≤ 3 %, Nb: ≤ 0.6 %, Ti: ≤ 0.3 %, V: ≤ 0.3 %, P: ≤ 0.1 %, B: ≤ 0.01 %, Mo: ≤ 0.3 %, N: ≤ 1.0 % and the remainder iron and unavoidable impurities, with zinc or a zinc alloy, comprising the following production steps: a) providing the flat steel product; b) annealing the flat steel product - at an annealing temperature Tg of 600 - 1100 °C, - for an annealing duration of 10 - 240 s under an annealing atmosphere having a reducing effect in relation to the FeO present on the flat steel product and having an oxidising effect in relation to the Mn contained in the steel substrate, this annealing atmosphere containing 0.01 - 85 % vol. H 2, H 2 O and N 2 and technically induced unavoidable impurities as the remainder and having a dew point which is between -70 °C and +60 °C, wherein for the H 2 O/H 2 ratio the following applies: 8 ⁢ x 10 − 15 * Tg 3.529 < H 2 O / H 2 ≤ 0.957, c) cooling the annealed flat steel product down to a bath entry temperature; d) passing the flat steel product, cooled down to the bath entry temperature, through a 420 - 520 °C hot Zn molten bath saturated with iron within a dipping time of 0.1 - 10 s, so that the flat steel product is hot-dip coated with a Zn protective coating which protects against corrosion, wherein the Zn molten bath consists of the main constituent zinc and unavoidable impurities, as well as0.05 - 8 % wt. Al and/or up to 8 % wt. Mg, as well as optionally Si < 2 %, Pb < 0.1 %, Ti < 0.2 %, Ni < 1 %, Cu < 1 %, Co < 0.3 %, Mn < 0.5 %, Cr < 0.2 %, Sr < 0.5 %, Fe < 3 %, B < 0.1 %, Bi < 0.1 %, Cd < 0.1 %; e) cooling the flat steel product flowing out of the molten bath and provided with the Zn coating. a) providing the flat steel product; b) annealing the flat steel product - at an annealing temperature Tg of 600 - 1100 °C, - for an annealing duration of 10 - 240 s under an annealing atmosphere having a reducing effect in relation to the FeO present on the flat steel product and having an oxidising effect in relation to the Mn contained in the steel substrate, this annealing atmosphere containing 0.01 - 85 % vol. H 2, H 2 O and N 2 and technically induced unavoidable impurities as the remainder and having a dew point which is between -70 °C and +60 °C, wherein for the H 2 O/H 2 ratio the following applies: 8 ⁢ x 10 − 15 * Tg 3.529 < H 2 O / H 2 ≤ 0.957, - at an annealing temperature Tg of 600 - 1100 °C, - for an annealing duration of 10 - 240 s under an annealing atmosphere having a reducing effect in relation to the FeO present on the flat steel product and having an oxidising effect in relation to the Mn contained in the steel substrate, this annealing atmosphere containing 0.01 - 85 % vol. H 2, H 2 O and N 2 and technically induced unavoidable impurities as the remainder and having a dew point which is between -70 °C and +60 °C, wherein for the H 2 O/H 2 ratio the following applies: 8 ⁢ x 10 − 15 * Tg 3.529 < H 2 O / H 2 ≤ 0.957, c) cooling the annealed flat steel product down to a bath entry temperature; d) passing the flat steel product, cooled down to the bath entry temperature, through a 420 - 520 °C hot Zn molten bath saturated with iron within a dipping time of 0.1 - 10 s, so that the flat steel product is hot-dip coated with a Zn protective coating which protects against corrosion, wherein the Zn molten bath consists of the main constituent zinc and unavoidable impurities, as well as0.05 - 8 % wt. Al and/or up to 8 % wt. Mg, as well as optionally Si < 2 %, Pb < 0.1 %, Ti < 0.2 %, Ni < 1 %, Cu < 1 %, Co < 0.3 %, Mn < 0.5 %, Cr < 0.2 %, Sr < 0.5 %, Fe < 3 %, B < 0.1 %, Bi < 0.1 %, Cd < 0.1 %; e) cooling the flat steel product flowing out of the molten bath and provided with the Zn coating.