The invention relates to a heat exchanger for vaporizing a coolant fluid by heat exchange with a calorigenic fluid, said exchanger comprising several parallel plates defining a plurality of passages between them which are suitable for the coolant fluid or calorigenic fluid to flow, a first wave and a second wave extending between two successive plates so as to define a plurality of channels within the same passage, said first and second waves comprising two adjacent edges, at least one assembly member extending from one edge to the other so as to connect the waves to one another. According to the invention, the assembly member is forcibly engaged in at least one part of a channel of the first wave on one hand, and in at least one part of a channel of the second wave on the other hand.