The invention relates to a heat exchanger, in particular a charge air cooler or exhaust gas cooler for an internal combustion engine of a motor vehicle, having a first box (2), a second box (3) which is arranged spaced apart from this first box (2), and a plurality of pipes (12) by means of which the first box (2) and the second box (3) are fluidically connected. Furthermore, the heat exchanger has a chamber (6) through which a coolant can flow and which is arranged between the two boxes (2, 3) and through which a plurality or all of these pipes (12), by means of which the two boxes (2, 3) are fluidically connected, run. The base (10, 11) is provided with one or more through-openings (16) for receiving the pipes (12), and at least one base (10, 11) has a border (7) which points away from the pipes toward the outside and is provided with a first step (20) and a second step (21), wherein the border (7) is arranged essentially in the edge region of the base (10, 11), and the second step (22) is arranged in the region of the first step (20), radially offset from the first step (20).