A method for applying a moisture barrier to a precipitator of cardboard for a two-step electrofilter, wherein the precipitator includes at least two paper bands (5) that constitute electrode elements in the precipitator, which paper bands (5) are multiply wound around a center axis of the precipitator, wherein the paper bands (5) exhibit a thin plastic layer with a thickness of 5-50 micrometers on their lateral surfaces (4), and where proximate electrode elements are arranged at a distance from one another in the radial direction of the precipitator. The method is characterized in that edge parts (6) of the paper bands (5) have a moisture-resistant substance applied to them. The material for fabricating a precipitator of cardboard for a two-step electrofilter is also described.