The invention relates to a dialysis machine capable of performing ultrafiltration without the need for a dedicated ultrafiltration pump. The system uses a pair of membrane flow balance pumps wherein the operation and/or the volume flow rate of the pumps can be modified during operation to bring about a net movement of dialysate either into or from the dialyser. The direction of flow of the dialysate in the dialyzer is reversible and the dialyzer can comprise two dialysate inlets, one at each end, and two dialysate outlets, one at each end.
