Self-supporting thin films containing nanopores are very promising materials for use for multiple applications, especially in nanofiltration. Here, we present a method for the production of nanomembranes containing a 3D ordered network of nanopores in an alumina matrix, with a diameter of about 1 nm and a body centered tetragonal structure of the network nodes. The material is produced by the magnetron sputtering deposition of a 3D ordered network of Ge nanowires in an alumina matrix, followed by a specific annealing process resulting in the evaporation of Ge. We demonstrate that the films can be easily grown on commercially available alumina substrates containing larger pores with diameters between 20 and 400 nm. We have determined the minimal film thickness needed to entirely cover the larger pores. We believe that these films have the potential for applications in the fields of filtration, separation and sensing.