Abstract: Plant for desalinating water of a water supply system, which comprises one or more tanks for accumulating water (2) in an immiscible manner, in order to store a softened supply thereof, provided with a first inlet connection (3) and with a first outlet connection (4) respectively connected to a feeding pipe (5) connected to the water supply system (50) and to an extraction pipe (6) for supplying users. The plant (1) also comprises a filtering unit (10) for water softening, for example obtained with a flow-through condenser (10?) or with a reverse osmosis membrane filter (10?), connected in parallel to the tank (2) with second inlet connection (1 1) and second outlet connection (12) respectively hydraulically connected to the first inlet connection (3) and to the first outlet connection (4) of the tank (2).