The heat exchanger is of the type comprising a stack of parallel plates and, between these plates, undulant spacers, each pair of plates defining a passage for fluid of generally flat shape. Certain passages (20) are subdivided over one part of their length into two closed subpassages (at 45, 57) at locations longitudinally offset relative to each other. The exchanger is applicable in cryogenic heat exchangers of installations for the distillation of air.