A semipermeable, porous, asymmetric membrane comprising a polyaramid containing, as structural repeating units, one or more structural units of the formula I' ##STR14## in which Ar is a divalent, aromatic or heteroaromatic radical, the two carbonyl groups being on non-adjacent ring carbon atoms and the Ar radical is optionally substituted by one or two branched or unbranched radicals selected from the group consisting of C.sub.1 -C.sub.3 -alkyl , C.sub.1 -C.sub.3 -alkoxy, aryl, aryloxy, C.sub.1 -C.sub.6 -perfluoroalkyl and C.sub.1 -C.sub.6 -perfluoroalkoxy radicals, fluorine, chlorine, bromine and/or iodine, and, based on the sum of (II') and (III'), to the extent of 50 to 100 mol %, structural units of the formula (II') ##STR15## in which X is a group --C(CH.sub.3).sub.2 --, --C(CF.sub.3).sub.2, --CO--, --SO--, --SO.sub.2 --, --CH.sub.2 --, --S--, or --O-- or a direct bond, and, based on the sum of (II') and (III') 0 to 50 mol %, structural units of the formula (III') ##STR16## the membrane being obtained by the phase inversion process, in which a homogeneous polymer solution is brought into contact with a precipitating bath containing a precipitating liquid, the precipitating liquid being miscible with the solvent of the polymer solution and the polymers dissolved in the polymer solution being precipitated as a membrane, wherein the polymer solution has a chloride content of less than 0.1% by weight, based on the total weight of the polymer solution.