Air-to-air heat exchanger for ventilation systems with two countercurrent air flows disposed inside a cylindrical housing, a first air flow circulating inside the heat exchanger inside closed pipes, whilst the second air flow is in spaces between the pipes and cylindrical housing, and a fan moving the countercurrent air flows and disposed at one end of the cylindrical housing, with the fan including concentric inner and outer rings separated by a wall for moving air in opposite directions, a bunch of straight, parallel pipes whose end elements at the fan side are tightly gathered together, in the end of a cylindrical wall and, on the opposite side, in the end of a cylindrical pipe fitting, and between end elements, taper into middle sections between which are spaces, and a sleeve lining the inner wall of the housing at the middle sections and constricts the inner diameter of the housing.