A filtration unit intended to allow the selective elimination of target substances from a fluid such as flood or a blood component, has an outer envelope formed from two flexible sheets joined together over their periphery along a bond line so as to define an inner volume, the envelope containing a filtering medium which delimits, on both sides of the bond line, an inlet compartment of the fluid to be filtered and an outlet compartment of the filtrate, each of the compartments being provided with an element—respectively an inlet and outlet element—for bringing the compartment into communication with the outside, the elements being connected between the sheets and comprising a flow channel that passes through the bond line, the unit being characterized in that at least one channel is offset relative to the bond line towards the compartment with which the channel is in communication.
