A filter unit includes membrane plates placed together parallel to one another, which at least in zones around connecting elements for the purpose of draining permeate are connected together liquid-tight. The membrane plates because of their shape and after two membrane plates have been placed one on top of the other are provided for manufacturing a liquid-tight connection or a seal by welding. As a result unfiltered liquid flows through between the membrane plates and contamination of the permeate within a volume situated between the connecting elements is prevented. Over a number of connecting elements and zones located in between it is possible to attach a hollow profile, which is closed-off at its ends. This hollow profile in a liquid-tight manner surrounds discharge openings of the connecting elements and the zones located in between with positive material engagement. As a result, a permeate collection channel is formed, out of which and through a permeate discharge the permeate can be extracted through suction.