A collector box (5) is a component of a heat exchanger for a motor vehicle, with the heat exchanger including a heat exchange core with a plurality of heat exchange tubes (3). The collector box (5) includes a fluid collector (9) with a flat bottom (13) to receive the ends of the tubes (3). The fluid collector (9) has two lateral walls (15) extending from the flat bottom (13) and respectively forming a curve between the lateral walls (15) and the flat bottom (13) of a radius (R) of between 1.5 and 4 mm. The fluid collector (9) has a ratio between the burst strength and the height (h) of the collector box (5) that is greater than 10.