A plate heat exchanger, in particular an oil cooler for internal combustion engines, in a stacking mode of construction, provides conduits projecting toward one side for formation of feeding and drainage channels. Each conduit typically is provided with an edge bent inwards and running parallel to the base of the neighboring plate. The collar forming the conduit projects sufficiently far from the base of the plate that the edge projecting inwards can abut the base of the neighboring plate. This configuration reduces the heat exchange surface. To eliminate this problem, instead of collars with an encircling edge projecting only toward one side, collars projecting toward both sides are provided. Each of the collars is formed conically and engages, on stacking, into another of the collars. The collars are formed identically, but on plates which, when set on one another, are turned 180° with respect to the other, thus making simple soldering and simple handling possible.