NOVELTY - Non-fresh water (1) is high-temperature electrolyzed, and hydrogen gas and oxygen gas are produced and separated. The separated gases are compressed, cooled and stored at elevated pressure. The gases are then combusted at elevated pressure to produce superheated steam at high temperature. The superheated steam is collected, heat is recovered from superheated steam, and at least some of the recovered heat is used as energy input. At least some of the superheated steam is condensed to produce fresh water (12).    USE - Conversion of non-fresh water e.g. seawater, brackish water, wastewater, polluted water, and water from source chosen from water from oil and gas production, flowback water from fracking, water production from tar sands, water from chemical/industrial/processing plants, and water from mining/foundries operations and oil spillage, to fresh water (all claimed). Uses include but are not limited to drinking, food preparation, bathing, washing clothes and dishes, flushing toilets, watering lawns and gardens, fresh water for hotels, restaurants, office, and civilian and military institutions, processing, cleaning, transportation, dilution and cooling in manufacturing facilities of steel, chemical and paper, in petroleum refining, production of electricity in thermoelectric power plants, irrigation of pasture and horticultural crops, water for stock animals, feed lots, dairies, and fish farms, and production of red meat, poultry, milk, eggs, and wool.    ADVANTAGE - The method involves combustion of hydrogen and oxygen at elevated pressure, which prevents air from entering the combustor and creation of nitrous oxide. The required heat for high-temperature electrolysis is obtained by capturing and utilizing heat which is generated by the combustion of hydrogen and oxygen. The method converts almost all of the input seawater to fresh water (conversion of 97% seawater and 3% salt/mineral into 97% fresh water and 3% salts/minerals). The elevated pressure reduces the volume required for high-temperature electrolysis and thus the volume of electrolysis units and in turn the number of high-temperature electrolysis units needed. The method also enables conversion of extracted heat into electricity.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) system for producing fresh water, consisting of a pretreatment unit for pre-treating non-fresh water, a high-temperature electrolysis unit (5) for receiving treated non-fresh water and for producing and separating hydrogen and oxygen gas from the treated non-fresh water, compressor (7A) for compressing hydrogen gas produced and separated by the electrolysis unit, compressor (8A) for compressing oxygen gas produced and separated by the electrolysis unit, a hydrogen and oxygen combustor (9) operable at elevated temperature and elevated pressure for producing superheated steam under high pressure temperature and pressure, and a collector connected to the combustor for collecting superheated steam produced by the combustor, and hermetically sealed to the combustor; and    (2) high-temperature electrolysis unit comprising a combustor, a collector, and a high-temperature electrolysis section.    DESCRIPTION OF DRAWING(S) - The drawing shows a flowchart of the high-temperature electrolysis of non-fresh water to produce fresh water.    Non-fresh water (1)    High-temperature electrolysis unit (5)    Non-water materials (6)    Compressors (7A,8A)    Storage tanks (7B,8B)    Combustor (9)    Heat exchanger (11)    Fresh water (12)