The fiter membrane comprises a porous structure made of a material selected from sintered ceramics, sintered metals, microporous carbon, and microporous glass, and is characterized by the fact that its entire external surface, including the inside surface of the pores in the structure, is covered with a thin and continuous film of carbon or of an oxide. In a sintered aluminum membrane, the surfaces of pores are coated with a dense and continuous thin layer of zirconia which prevents the surfaces from being degraded in service. In the figure, curve 3 shows how the throughput of a membrane without a zirconia layer falls off over time, while curve 4 shows little change in the same membrane having such a layer.