Method of producing a precoated steel sheet comprising the successive steps of: - providing a precoated steel strip comprising a steel substrate having, on at least one of its main faces, a precoating, the precoating comprising an intermetallic alloy layer and a metallic alloy layer extending atop the intermetallic alloy layer, the metallic alloy layer being a layer of aluminum, a layer of aluminum alloy or a layer of aluminum-based alloy, - laser cutting said precoated steel strip so as to obtain at least one precoated steel sheet, said precoated steel sheet comprising a cut edge surface resulting from the cutting operation, the cut edge surface comprising a substrate region and a precoating region and the thickness of the precoated steel sheet being comprised between 0.8 mm and 5 mm, characterised in that the laser cutting is carried out such that it results directly in a corrosion-improved zone of the cut edge surface, extending over the entire height (h) of the cut edge surface and over a length smaller than or equal to the length of the cut edge surface, the surface fraction (S Total) of aluminum on the substrate region of the corrosion-improved zone of the cut edge surface directly resulting from the laser cutting operation being greater than or equal to 9% and the surface fraction (S Bottom) of aluminum on the bottom half of the substrate region of the corrosion-improved zone of the cut edge surface directly resulting from the laser cutting operation being greater than or equal to 0.5%, wherein the laser cutting step is performed using an inert gas as an assist gas, wherein the laser cutting step is performed using a CO 2 laser, and wherein, in order to obtain the corrosion-improved zone, the laser cutting is performed using a laser cutting linear energy E comprised between 0.18 kJ/cm and 0.29 kJ/cm and an assist gas pressure P comprised between P min = 54.5 × E - 7.8 bars and P max, whereby P max is equal to 14 bars for E ≤ 0.24 kJ/cm and P max is equal to -80 × E + 33.2 bars for E > 0.24 kJ/cm. - providing a precoated steel strip comprising a steel substrate having, on at least one of its main faces, a precoating, the precoating comprising an intermetallic alloy layer and a metallic alloy layer extending atop the intermetallic alloy layer, the metallic alloy layer being a layer of aluminum, a layer of aluminum alloy or a layer of aluminum-based alloy, - laser cutting said precoated steel strip so as to obtain at least one precoated steel sheet, said precoated steel sheet comprising a cut edge surface resulting from the cutting operation, the cut edge surface comprising a substrate region and a precoating region and the thickness of the precoated steel sheet being comprised between 0.8 mm and 5 mm, characterised in that the laser cutting is carried out such that it results directly in a corrosion-improved zone of the cut edge surface, extending over the entire height (h) of the cut edge surface and over a length smaller than or equal to the length of the cut edge surface, the surface fraction (S Total) of aluminum on the substrate region of the corrosion-improved zone of the cut edge surface directly resulting from the laser cutting operation being greater than or equal to 9% and the surface fraction (S Bottom) of aluminum on the bottom half of the substrate region of the corrosion-improved zone of the cut edge surface directly resulting from the laser cutting operation being greater than or equal to 0.5%, wherein the laser cutting step is performed using an inert gas as an assist gas, wherein the laser cutting step is performed using a CO 2 laser, and wherein, in order to obtain the corrosion-improved zone, the laser cutting is performed using a laser cutting linear energy E comprised between 0.18 kJ/cm and 0.29 kJ/cm and an assist gas pressure P comprised between P min = 54.5 × E - 7.8 bars and P max, whereby P max is equal to 14 bars for E ≤ 0.24 kJ/cm and P max is equal to -80 × E + 33.2 bars for E > 0.24 kJ/cm.