A heat exchanger with a heat-exchange core in which a first fluid and a second fluid circulate, at least one header tank configured to duct the second fluid from or to the heat-exchange core. The header tank has at least a shoulder oriented toward the outside of said header tank, and at least one header tank corner. At least one fastening member for fastening the header tank is positioned at least partly at the periphery of the heat-exchange core and includes at least one peripheral groove delimited by a base wall and a lateral wall and in which the shoulder of the header tank is at least partially housed. Part of the corner portion faces an upper face of the shoulder opposite to the groove of the fastening member and at a non-zero distance from this upper face so that a space is left between the corner portion and the upper face of the shoulder.