(57) Method of immobilizing nuclear waste in an aqueous slurry which contains sodium sulfate. The water evaporated from the slurry and the resulting concentrate is mixed with from 50 to 200% by weight based on the sodium sulfate weight of a destabilizing compound which contains a metal which forms an unstable sulfate and from 5 to 20% by weight based on a total weight of the sodium sulfate in the destabilizing compound of a reducing agent. The mixture is heated at from 700 to 900°C to decompose the sulfate and evolve the resulting sulfurous gases. After cooling, glass formers are added to the concentrate in a weight ratio of from 1 to 2. The concentrate is heated to from 1050 to 1200°C to form a homogeneous melt. The melt is cooled, packaged, labeled, and transported to storage.