The invention relates to a stacked plate heat exchanger, comprising a plurality of elongate plates which are stacked on one another and connected to one another and which have a corrugated profile, which plates have a cavity for leading through a medium to be cooled in the longitudinal direction of the plates and define a further cavity for leading through a coolant, wherein leadthrough openings for supplying or discharging the medium to be cooled or the coolant are formed approximately in the end regions of each elongate plate and each elongate plate is surrounded by a bent-off edge, wherein an nth corrugation of the corrugated profile of each plate is drawn close to the edge, preferably into the edge, whereas the other corrugations of the corrugated profile of the plate terminate before the edge, where n=2, 3, 4 etc.