A method of manufacturing a coated and hardened steel part, comprising the successive steps of: - a pre-coated cold rolled and annealed sheet is provided for the manufacture of press-hardened parts, consisting of a heat treatment steel substrate containing a carbon content Co of between 0.07% and 0.5%, said content being expressed by weight, and a metallic pre-coating on at least the two main faces of said steel substrate, said metallic pre-coating being aluminium or an aluminium alloy, or zinc or a zinc alloy, or is composed of a layer of aluminium or an aluminium alloy, surmounted by a layer of zinc or a zinc alloy, the composition of said steel substrate comprising, the contents being expressed by weight: 0.07% ≤ C ≤ 0.5% 0.5% ≤ Mn ≤ 3% 0.02% ≤ Si ≤ 0.5% 0.01% ≤ Cr ≤ 1% Ti ≤ 0.2% Al ≤ 0.25% S ≤ 0.05% P ≤ 0.1% 0.0005% ≤ B ≤ 0.010%, optionally 0.0005% ≤ Ca ≤ 0.005%, the remainder of the composition consisting of iron and unavoidable impurities resulting from the smelting method, said substrate having a decarburised zone on the surface of each of said two main faces, the depth p 50% of said decarburised zone being between 6 and 30 micrometres p 50% being the depth at which the carbon content is equal to 50% of said C 0 content, the depth p 50% being measured by glow discharge spectroscopy, said sheet not containing an iron oxide layer between said substrate and said metallic pre-coating, - the said pre-coated sheet is cut to obtain a blank, then - the said blank is optionally cold-drawn, then - said blank is heated to a temperature TR in a furnace so as to impart, at least partially, an austenitic structure to said steel, and then - the heated blank is removed from the furnace and transferred to a press or shaping device, and - the said blank is hot-deformed or hot-gauged to obtain a part, then - the said part is cooled within the said press or the said shaping device in order to give it a martensitic or bainito-martensitic microstructure by hardening. - a pre-coated cold rolled and annealed sheet is provided for the manufacture of press-hardened parts, consisting of a heat treatment steel substrate containing a carbon content Co of between 0.07% and 0.5%, said content being expressed by weight, and a metallic pre-coating on at least the two main faces of said steel substrate, said metallic pre-coating being aluminium or an aluminium alloy, or zinc or a zinc alloy, or is composed of a layer of aluminium or an aluminium alloy, surmounted by a layer of zinc or a zinc alloy, the composition of said steel substrate comprising, the contents being expressed by weight: 0.07% ≤ C ≤ 0.5% 0.5% ≤ Mn ≤ 3% 0.02% ≤ Si ≤ 0.5% 0.01% ≤ Cr ≤ 1% Ti ≤ 0.2% Al ≤ 0.25% S ≤ 0.05% P ≤ 0.1% 0.0005% ≤ B ≤ 0.010%, optionally 0.0005% ≤ Ca ≤ 0.005%, the remainder of the composition consisting of iron and unavoidable impurities resulting from the smelting method, said substrate having a decarburised zone on the surface of each of said two main faces, the depth p 50% of said decarburised zone being between 6 and 30 micrometres p 50% being the depth at which the carbon content is equal to 50% of said C 0 content, the depth p 50% being measured by glow discharge spectroscopy, said sheet not containing an iron oxide layer between said substrate and said metallic pre-coating, 0.07% ≤ C ≤ 0.5% 0.5% ≤ Mn ≤ 3% 0.02% ≤ Si ≤ 0.5% 0.01% ≤ Cr ≤ 1% Ti ≤ 0.2% Al ≤ 0.25% S ≤ 0.05% P ≤ 0.1% Ti ≤ 0.2% Al ≤ 0.25% S ≤ 0.05% P ≤ 0.1% 0.0005% ≤ B ≤ 0.010%, - the said pre-coated sheet is cut to obtain a blank, then - the said blank is optionally cold-drawn, then - said blank is heated to a temperature TR in a furnace so as to impart, at least partially, an austenitic structure to said steel, and then - the heated blank is removed from the furnace and transferred to a press or shaping device, and - the said blank is hot-deformed or hot-gauged to obtain a part, then - the said part is cooled within the said press or the said shaping device in order to give it a martensitic or bainito-martensitic microstructure by hardening.