A specially developed plasma process enables the production of hollow fiber membranes that permit single-stage dialysis. The hollow fibers are functionalized in such a way that the sensitive blood cells are washed unhindered through the unmodified lumens of the hollow fibers. The blood plasma, on the other hand, is filtered through the pores of the membrane. Their surface is functionalized in such a way that inflammatory endotoxins such as lipopolysaccharides (LPS) adhere to it. The new process puts considerably less strain on the patient because a substantially smaller part of the blood volume is located outside the body than in the conventional two-stage blood purification process.