When applying a method and an arrangement for purifying water, an inflow of contaminated water is converted to a pressure elevated flow which is divided in a purifying unit into a purified outflow and a contaminated outflow, which in turn is divided into a return flow and a reject flow. With the intention of providing a large return flow under high pressure for the purpose of rinsing clean the filter unit during operation, it is proposed in accordance with the invention, among other things, that the return flow includes a first return flow (return conduit 24) which is recycled to the pressure-elevated flow (pressure conduit 16) and which is essentially larger than the inflow, and further includes a second return flow (return conduit 34) which is pressure-restricted (pressure-limiting valve 28) with respect to the first return flow, and the second return flow is returned to the inflow (inlet conduit 14).