Abstract: In a method of welding a thin titanium tube to a titanium or titanium clad header of a heat exchanger, the titanium tube is inserted into a hole formed through the header and then the body portion of a core is inserted into the hole of the header. The core is provided with a support and a circular flange at a joint between the body portion and the support. The flange is provided with a notch extending radially inwardly of the flange. When the core is inserted into the hole of the header, the flange comes to engage the header and then the front end of an electrode is positioned in the notch to generate an electric arc, while rotating the core or only the flange, between the front end of the electrode and a portion of the header radially separated by a predetermined distance from the titanium tube. Thus, the header and the titanium tube are melted and welded by the arc.