Abstract: The aim of the present invention is a process for preparing a mineral matrix by melting, which is implemented according to the method of direct cold crucible induction melting. The method employs a step for initiating the melting. During the initiation step, a conductive mineral load is generated, by introduction of constituent elements of the matrix, into a bath of a conductive liquid, brought by induction to a suitable temperature, in the cold crucible. The intervening conductive liquid has the property of being a liquid and an electric conductor at a temperature between &thgr;1 of less than 600° C., advantageously of between 100 and 500° C., and a temperature &thgr;2 at least equal to the temperature at which the constituent elements of the matrix melt to generate the matrix. The conductive liquid is advantageously a molten sodium hydroxide bath. The preparation of such a glass matrix is advantageously implemented within the context of a method of vitrifying radioactive waste materials.