Abstract: A method for manufacturing a steel sheet provided with a coating included from 0.80 to 1.40 wt. % of Al, from 0.80 to 1.40 wt. % of Mg, unavoidable impurities and optionally one or more additional elements selected from Si, Sb, Pb, Ti, Ca, Mn, Sn, La, Ce, Cr, Zr or Bi, the weight content of each additional element in the coating being less than 0.3%, the remainder being Zn, the outer surface of the coated steel sheet having a waviness Wa0.8 before skin-pass of less than or equal to 0.50 ?m; the coated steel sheet obtained by this method; the part obtained by deformation of a steel sheet and a land motor vehicle comprising a body, the body including the part.