A method for producing a zinc or zinc-alloy coated steel sheet with a tensile strength higher than 900 MPa, for the fabrication of resistance spot welds containing in average not more than two Liquid Metal Embrittlement cracks per weld having a depth of 100μm or more, comprising the successive steps of: - providing a cold-rolled steel sheet, the nominal composition of which contains, in weight percent: 0.07% ≤ C ≤ 0.5% 0.3% ≤ Mn ≤ 5% 0.010% ≤ Al ≤1% 0.010% ≤ Si ≤2.45% with 0.35% ≤ (Si+Al) ≤ 2.5%, 0.001% ≤ Cr ≤ 1.0% 0.001% ≤ Mo ≤ 0.5% and optionally 0.005% ≤ Nb ≤0.1% 0.005% ≤ V ≤ 0.2% 0.005% ≤ Ti ≤ 0.1% 0.0001% ≤ B ≤ 0.004% 0.001% ≤ Cu ≤ 0.5% 0.001% ≤ Ni ≤ 1.0%, the remainder being iron and unavoidable impurities from the smelting, in contents such as: S<0.003% P<0.02% N<0.008%, - heating said cold-rolled steel sheet up to a temperature T1 comprised between 550°C and Ac1+50°C in a furnace zone with an atmosphere A1 containing from 2 to 15% hydrogen by volume, the balance being nitrogen and unavoidable impurities, so that the iron is not oxidized, then - adding in the furnace atmosphere, at least one element selected from water steam or oxygen with an injection flow rate Q higher than 0.07%/h x α α being equal to 1 if said element is water steam or equal to 0.52 if said element is oxygen, at a temperature T≥T1, so to obtain an atmosphere A2 with a dew point DP2 comprised between -15°C and the temperature Te of the iron/iron oxide equilibrium dew point, wherein the injection rate Q is the injected volume of water steam or oxygen per hour divided by the volume of the furnace between the injection location of water steam or oxygen, and the end of the furnace section heated at the soaking temperature T2, - heating the sheet from said temperature T 1 up to a temperature T 2 comprised between 720°C and 1000°C in a furnace zone under an atmosphere A2 of nitrogen containing from 2 to 15% hydrogen, more than 0.1% CO by volume, with an oxygen partial pressure higher than 10 -21 atm., wherein the duration t D of said heating of the sheet from temperature T 1 up to the end of soaking at temperature T 2 is comprised between 100 and 500s, - soaking the sheet at T 2, then - cooling the sheet at a rate comprised between 10 and 400°C/s, then - coating the sheet with zinc or zinc-alloy coating. - providing a cold-rolled steel sheet, the nominal composition of which contains, in weight percent: 0.07% ≤ C ≤ 0.5% 0.3% ≤ Mn ≤ 5% 0.010% ≤ Al ≤1% 0.010% ≤ Si ≤2.45% with 0.35% ≤ (Si+Al) ≤ 2.5%, 0.001% ≤ Cr ≤ 1.0% 0.001% ≤ Mo ≤ 0.5% and optionally 0.005% ≤ Nb ≤0.1% 0.005% ≤ V ≤ 0.2% 0.005% ≤ Ti ≤ 0.1% 0.0001% ≤ B ≤ 0.004% 0.001% ≤ Cu ≤ 0.5% 0.001% ≤ Ni ≤ 1.0%, the remainder being iron and unavoidable impurities from the smelting, in contents such as: S<0.003% P<0.02% N<0.008%, 0.07% ≤ C ≤ 0.5% 0.3% ≤ Mn ≤ 5% 0.010% ≤ Al ≤1% 0.010% ≤ Si ≤2.45% with 0.35% ≤ (Si+Al) ≤ 2.5%, 0.001% ≤ Cr ≤ 1.0% 0.001% ≤ Mo ≤ 0.5% and optionally 0.005% ≤ Nb ≤0.1% 0.005% ≤ V ≤ 0.2% 0.005% ≤ Ti ≤ 0.1% 0.0001% ≤ B ≤ 0.004% 0.001% ≤ Cu ≤ 0.5% 0.001% ≤ Ni ≤ 1.0%, S<0.003% P<0.02% N<0.008%, - heating said cold-rolled steel sheet up to a temperature T1 comprised between 550°C and Ac1+50°C in a furnace zone with an atmosphere A1 containing from 2 to 15% hydrogen by volume, the balance being nitrogen and unavoidable impurities, so that the iron is not oxidized, then - adding in the furnace atmosphere, at least one element selected from water steam or oxygen with an injection flow rate Q higher than 0.07%/h x α α being equal to 1 if said element is water steam or equal to 0.52 if said element is oxygen, at a temperature T≥T1, so to obtain an atmosphere A2 with a dew point DP2 comprised between -15°C and the temperature Te of the iron/iron oxide equilibrium dew point, wherein the injection rate Q is the injected volume of water steam or oxygen per hour divided by the volume of the furnace between the injection location of water steam or oxygen, and the end of the furnace section heated at the soaking temperature T2, - heating the sheet from said temperature T 1 up to a temperature T 2 comprised between 720°C and 1000°C in a furnace zone under an atmosphere A2 of nitrogen containing from 2 to 15% hydrogen, more than 0.1% CO by volume, with an oxygen partial pressure higher than 10 -21 atm., wherein the duration t D of said heating of the sheet from temperature T 1 up to the end of soaking at temperature T 2 is comprised between 100 and 500s, - soaking the sheet at T 2, then - cooling the sheet at a rate comprised between 10 and 400°C/s, then - coating the sheet with zinc or zinc-alloy coating.