An electrodialysis machine for desalinating water with a high concentration of dissolved salts, comprising, between two heads (11, 12), two opposite electrode chambers (13, 14), which contain electrodes (15, 16) having opposite polarities, between which a plurality of reaction chambers of two alternating types are arranged, first ionic enrichment chambers and second ionic depletion chambers, each chamber of a first type being open onto a laterally adjacent chamber of the second type by interposition of an ion-conducting membrane (19, 20), said first chambers being hydraulically connected to each other and to said heads so as to form a first hydraulic circuit for the transit of a first water flow with ionic enrichment, said second chambers being hydraulically connected to each other and to said heads so as to form a second hydraulic circuit for the transit of a second water flow, which is being desalinated, hydraulic means for the exchange of first and second water flows being provided, each electrode chamber (13, 14) being supplied by a corresponding independent hydraulic circuit (25, 26), each one of the electrode chambers (13, 14) being formed directly against the adjacent distribution head (11, 12) and comprising the flat electrode (15, 16), which is made of biplanar metallic mesh, said electrode (15, 16) being arranged within a first flat sealing gasket (33, 76), which is provided with first holes (34, 35), to be understood as part of the hydraulic circuit (25, 26) associated with the electrode (15, 16), for the entry and the exit of the water pumped by a dedicated pump (36, 83), in said first sealing gasket second holes (37, 38) being also provided for the passage of the water flows (22, 24), which cooperate in defining the first and second hydraulic circuits, adjacent to the first gasket a second distribution gasket (39, 77) being positioned, which is provided with first distribution holes which are open toward the inside of the second gasket (39, 77) so as to form nozzles for introducing the water flow inside the electrode chamber (13, 14), and first discharge manifold holes which are formed on the opposite side of the second gasket (39, 77) and are also open toward the inside of said second gasket (39, 77), said second gasket (39, 77) having second holes (42, 43) for the passage of the water flows (22, 24), which cooperate in defining the first and second hydraulic circuits, inside the second gasket (39, 77) there being provided a biplanar mesh (44, 81), which is adapted to promote turbulence in the electrode chamber (13, 14), an ion-conducting shielding membrane (45, 79) being arranged in contact with the second gasket (39, 77) and with the biplanar mesh (44, 81) and being adapted to prevent the migration, to the adjacent reaction chambers (17, 18), of any unwanted products of the electrolytic reactions that occur at the electrode, said shielding membrane (45, 79) being closed between the second gasket (39, 77) and a third similar distribution gasket (50, 80), inside the third gasket (50, 80) a second biplanar mesh (55, 82) being provided, which is adapted to promote the turbulence of the water flow in transit, said electrode chamber (13, 14) terminating in a first, active ion-conducting membrane (19, 20), said first ion-conducting membrane (19, 20) having only holes (56, 57) for the passage of the water flows (22, 24), which cooperate in defining the first and second hydraulic circuits, whereas there are no holes at the first holes of the adjacent third gasket (50, 80) for the transit of the water flow of the hydraulic circuit (25, 26) associated with the electrolytic chamber (13, 14), said water flow being thus contained within the third gasket (50, 80), and each reaction chamber (17, 17a, 17b, 17c, 17d, 18, 18a, 18b) comprising, between two first and second ion-conducting membranes, an interposed diffusion gasket (58, 66), which has on one side first contoured openings (59, 69) for the inlet of a flow of water and, on the opposite side, second contoured openings (60, 68) for the outlet of said water flow from the reaction chamber, said contoured openings (59, 60, 68, 69) being formed at the overlying holes (56, 57, 64, 65) of the adjacent ion-conducting membranes, in alternation with the contoured openings (59, 60, 68 69), in the diffusion gaskets (58, 66), transit holes (61, 62, 70, 71) being provided which are adapted to allow the passage of the water flows toward the underlying reaction chambers.