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 100 μm or more, with steps of providing a cold-rolled steel sheet, heating cold-rolled steel sheet up to a temperature T1 between 550° C. and Ac1+50° C. in a furnace zone with an atmosphere (A1) containing from 2 to 15% hydrogen by volume, so that the iron is not oxidized, then adding in the furnace atmosphere, water steam or oxygen with an injection flow rate Q higher than (0.07%/h×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 between −15° C. and the temperature Te of the iron/iron oxide equilibrium dew point, then heating the sheet from temperature T1 up to a temperature T2 between 720° C. and 1000° C. in a furnace zone under an atmosphere (A2) of nitrogen containing from 2 to 15% hydrogen and more than 0.1% CO by volume, with an oxygen partial pressure higher than 10−21 atm., wherein the duration to of heating of the sheet from temperature T1 up to the end of soaking at temperature T2 is between 100 and 500 s, soaking the sheet at T2, then cooling the sheet at a rate between 10 and 400° C./s, then coating the sheet with zinc or zinc-alloy coating.