The invention relates to a method for forming a highly electroconductive surface on an aluminum piece. A highly conductive layer of silver is formed on the piece by means of a eutectic join. The temperature of the aluminum piece is raised gradually and the oxide layer formed on the surface of the piece is removed. After the first heating stage, the silver piece that is to be attached is transferred to the cleaned surface. The contact point is heated to a temperature where a eutectic bond is generated between the aluminum and silver. During the second heating stage a slight momentary loading is applied to the contact point.