The invention relates to a method for producing a hydrolytically stable polyamide membrane having an open-pored, microporous and sponge-like support-layer structure, using a process involving thermally induced liquid-liquid phase separation. A solution of an aliphatic polyamide in a solvent system, comprising preferably a solvent and a non-solvent for the polyamide, is extruded to form a shaped object. After leaving the die, the shaped object is cooled by means of a cooling medium until phase separation occurs and the polymer-rich phase solidifies to form the membrane structure. The solution of the polyamide in the solvent system contains an antioxidant agent as a stabiliser for the polyamide which, together with the solvent system, is selected in a way that the antioxidant agent is essentially insoluble in the solvent system at the phase separation temperature. The invention also relates to a polyamide membrane with improved hydrolytic stability, characterised in that it contains an antioxidant agent as a stabiliser for improving hydrolytic stability.