A circulation pump and an electrochemical ozone generator are integrated into the permeate return line of an RO system, and the permeate return line is connected in flow direction behind the circulation pump and the ozone generator by a recirculation line to the permeate supply line, which can form a closed circuit where the ozonized permeate circulates until all organic contaminants have been killed or decomposed by the ozone in that part of the line system. Valves are integrated, respectively, into the recirculation line and the permeate return line downstream of the branch of the recirculation line. During normal operation of the RO system, the recirculation line valve is connected for feeding connected dialysis devices while the permeate return line valve is open, so excessive permeate that was not taken by the dialysis devices can flow into the supply tank. Alternatively, the permeate can be discharged into an outlet.