A flat steel product, intended to be formed into a component by hot press forming and having a base made of steel, onto which a metal anti-corrosion coating of a Zn or a Zn alloy is applied. A separate finishing coat is applied to at least one of the free surfaces of the flat steel product. The finishing coat includes at least one base metal compound (oxide, nitride, sulphide, sulphate, carbide, carbonate, fluoride, hydrate, hydroxide, or phosphate). Also, a method enabling the production of a flat steel product of this kind.