The invention relates to a heat exchanger with a channel (4) through which cooling agent flows and a channel (3) through which fluid to be cooled flows, whereby ribs (6) project into at least one of the channels (3, 4). According to the invention, these ribs (6) feature a linear approach edge (11) and a linear flow-off edge (15), whereby the side walls (12) run continuously between the approach edge (11) and the flow-off edge (15). By these means it is achieved that a turbulent boundary layer forms at the ribs, which boundary layer ends in a turbulent eddy in the area of the flow-off edge (15). This leads to an increased efficiency of the heat exchanger and simultaneously to a good homogenization of the fluid. Moreover, sooting is reliably avoided.