Plant for desalinating water of a water supply system, characterized in that it comprises: - at least one tank for accumulating water in an immiscible manner, susceptible of storing a softened water supply, provided with a first inlet connection and with a first outlet connection respectively connected to a feeding pipe connected to the water supply system in order to supply the plant with water from the water supply system, and to an extraction pipe, which transports the water flow intended for use and is intercepted by at least one tap; - at least one filtering unit for water softening provided with a second inlet connection and with a second outlet connection, connected in parallel to said tank for accumulating water in an immiscible manner, with said second inlet connection and second outlet connection respectively hydraulically connected to said first inlet connection and to said first outlet connection of said tank for accumulating water in an immiscible manner; - circulating means which can be activated to force at least one water flow to be treated to pass from said second inlet connection to said second outlet connection through said filtering unit, producing a filtered water flow which flows through said first outlet connection, being progressively stored with a corresponding volume of filtered water in said tank for accumulating water in an immiscible manner according to a filling direction of the latter directed from said first outlet connection to said first inlet connection; - the feeding pipe of said water supply system forcing, with said tap at least partially open, a water flow intended for use to flow through said tank for accumulating water in an immiscible manner from said first inlet connection to said first outlet connection towards said extraction pipe, causing the at least partial evacuation of said filtered water volume stored in said tank for accumulating water in an immiscible manner in an evacuation direction opposite said filling direction, so that with said tap open, there being a water flow request by an user, said filtering unit is by-passed and the flow of water from said water supply system is sent to said tank, forcing the liquid volume contained therein to be discharged towards said extraction pipe with said evacuation direction opposite said filling direction, so that the final volume of filtered water to be accumulated in said tank is the first to be sent to the user. - at least one tank for accumulating water in an immiscible manner, susceptible of storing a softened water supply, provided with a first inlet connection and with a first outlet connection respectively connected to a feeding pipe connected to the water supply system in order to supply the plant with water from the water supply system, and to an extraction pipe, which transports the water flow intended for use and is intercepted by at least one tap; - at least one filtering unit for water softening provided with a second inlet connection and with a second outlet connection, connected in parallel to said tank for accumulating water in an immiscible manner, with said second inlet connection and second outlet connection respectively hydraulically connected to said first inlet connection and to said first outlet connection of said tank for accumulating water in an immiscible manner; - circulating means which can be activated to force at least one water flow to be treated to pass from said second inlet connection to said second outlet connection through said filtering unit, producing a filtered water flow which flows through said first outlet connection, being progressively stored with a corresponding volume of filtered water in said tank for accumulating water in an immiscible manner according to a filling direction of the latter directed from said first outlet connection to said first inlet connection; - the feeding pipe of said water supply system forcing, with said tap at least partially open, a water flow intended for use to flow through said tank for accumulating water in an immiscible manner from said first inlet connection to said first outlet connection towards said extraction pipe, causing the at least partial evacuation of said filtered water volume stored in said tank for accumulating water in an immiscible manner in an evacuation direction opposite said filling direction, so that with said tap open, there being a water flow request by an user, said filtering unit is by-passed and the flow of water from said water supply system is sent to said tank, forcing the liquid volume contained therein to be discharged towards said extraction pipe with said evacuation direction opposite said filling direction, so that the final volume of filtered water to be accumulated in said tank is the first to be sent to the user.