A method for manufacturing a high temperature electrolyzer (HTE) or a high temperature fuel cell is disclosed. According to one aspect, the HTE includes a vertical stack of n elementary planar cells alternating with n+1 interconnection plates. Each of the elementary cells include a planar porous anode and a planar porous cathode each having cutouts formed therein. The anode and cathode are respectively positioned on each of the faces of a planar dense electrolyte. Brazed joints are formed by infiltration of a defined amount of a brazing composition in the electrodes at contact points between the elementary cells and the interconnection plates.