A heat exchanger for exchange of heat between a first fluid and a second fluid comprises a stack of pockets (1) mutually aligned in a longitudinal direction and having two header boxes (16, 17) that are mutually juxtaposed in a lateral direction. The first fluid is injected into an upstream connecting channel (12) by a longitudinal nozzle (22) passing through a heat exchanger end face (5) remote from the upstream connecting channel, and at least one other connecting channel (14). This longitudinal nozzle has a cross section of oblong general shape, whose greatest dimension is parallel to the greatest dimension of the pockets. The heat exchanger may be produced particularly in the form of an evaporator for an air-conditioning device for the passenger compartment of a vehicle.