The invention relates to a membrane for the separation of material mixtures by the principle of vapor permeation or pervaporation, in particular for the dewatering of organic solvents, comprising at least one support layer and at least one material-selective separation layer located thereon, and a method for production of such a membrane. The material-selective separating layer is made from polyvinyl alcohol, containing at least one metallic element and/or a derivative thereof. The method includes the addition of polyvinyl alcohol to a solvent, adding an organometallic compound to the solvent/polyvinyl alcohol mixture, and then applying the solvent/polyvinyl alcohol/organometallic compound mixture to the support layer as the material-selective separating layer.