The invention concerns a heat exchanger which includes a stack of plates defining passages, containing corrugated fins which include a transverse section with repeated corrugated pattern extending between two upper and lower end planes. The pattern includes a base corrugated pattern that includes corrugated legs linked to corrugated summits and corrugated bases, this base pattern being modified by a sub-pattern which defines, between at least some corrugated legs, additional leading edges located at an intermediate level between the end planes. The invention is applicable to cryogenic gas--gas heat exchangers.