Abstract: Method for welding two end portions (6, 8) of a coil (not shown) onto two electric contact pads or bumps (24, 26) of an integrated circuit (2) or an electronic unit of small dimensions. This welding method is characterised in that, prior to the actual welding step, a preliminary step is provided consisting in removing at least partially the insulating sheath from the electric wire (10) at least at the locations of the two end portions (6, 8) provided for the welding onto said electric contact pads or bumps (24, 26). The insulating sheath is removed locally by means of heat application, in particular using a heating press (58) working at a sufficiently high temperature to melt or sublimate the insulating sheath. The welding step is achieved at a much lower temperature than the temperature of the preliminary step, which allows the heat and mechanical stress to be reduced for the integrated circuit (2) and the bumps (24, 26) during welding of the ends (6, 8) onto said bumps.