For a hot-dip coated, flat steel product, optimal wetting and adhesion of the hot dip coating are achieved by preoxidation in a DFF preheating furnace and humidification of the annealing atmosphere in a holding zone. First, the flat steel product, which is present at a temperature of 550 - 850 °C, is exposed to an oxidising atmosphere, which is introduced by injecting an oxygen-containing gas stream into the flame of a burner, for 1 - 15 s in a preoxidation section of the DFF furnace in order to form a covering FeO layer on the surface thereof, whereas a reduced or neutral atmosphere with respect to the steel surface prevails outside the preoxidation section in the DFF furnace. The flat steel product, which has been heated to a holding temperature of 600 - 1100 °C, is then annealed in a recrystallising manner under an FeO-reducing atmosphere, the dew point of which is held at -40 °C to +25 °C by the addition of moisture, cooled to a bath entry temperature of 420 - 780 °C under an atmosphere having ≤100 % N2 and a dew point of -80 °C bis -25 °C, and passed through a melt bath.