A method for welding two metal parts, in which: the metal parts are positioned against each other in a welding position, the parts being respectively in surface contact along their welding surfaces, at least one of the parts having at least one extra-thick zone along its welding surface; TIG welding is carried out on the welding surfaces (v) of the metal parts by means of a TIG welding torch, a method in which a penetrating welding flux is applied locally on said extra-thick zone of the metal part prior to the TIG welding step.