Disclosed is a method for producing a permanently joined plate heat exchanger comprising a plurality of metal heat exchanger plates having a solidus temperature above 1100° C., provided beside each other and forming a plate package with first plate interspaces for a first medium and second plate interspaces for a second medium, wherein the first and second plate interspaces are provided in an alternating order in the plate package, wherein each heat exchanger plate comprises a heat transfer area and an edge area comprising bent edges which extend around the heat transfer area, wherein a first surface of the plates forms a convex shape and a second surface of the plates forms a concave shape, wherein the heat transfer area comprises a corrugation of elevations and depressions, wherein said corrugation of the plates and the bent edges are provided by pressing the plates. Also disclosed is a plate heat exchanger produced by the method.