In an electrolytic cell a membrane consisting of dielectric material such as an organic polymer, which separates two chambers of the electrolytic cell from each other is produced using an etching solution which is provided in one of the chambers, contains active etching ions, while the other chamber contains a solution, which does not have an etching action. An electrical field is generated through the membrane. The etching progresses along ion tracks in the membrane and first produces one funnel-shaped pore per ion track. Immediately prior to the breakthrough, the ions, which do not have an etching action, begin to penetrate the still existent thin layer with fine pores—the active layer—and displace the ions with an etching action. An intensified electric current, driven by the adjacent field, is established and the etching process at the bottom of the pore shifts sideways according to the concentration of etching ions still present. The process is stopped by deactivating the field and flushing the membrane.