PURPOSE: To convert a material contained in waste water into nitrogen, carbon dioxide, water and ash to make the waste water harmless by wet-oxidizing the waste water contg. silver nitrate with a specified catalyst under specified pressure conditions in the presence of a reducing agent.

CONSTITUTION: A solid catalyst contg. a compd. selected from a group consisting of manganese, iron and cobalt as a catalytic component A, a compd. selected from a group consisting of titanium, silicon and zirconium as a catalytic component B and a compd. selected from a group consisting of cerium, tungsten, copper, silver, gold, platinum, palladium, rhodium, ruthenium and iridium as a catalytic component C is packed in a wet oxidation reaction tower 1 into which a nitrate radical-contg. waste water is introduced. The waste water contg. nitrate radical is wet-oxidized in the presence of a reducing agent in the amt. more than the equivalent to reduce the nitrate radical to nitrogen under the pressure conditions where the waste water is kept a liq. phase at the reduction temp. of 100-370°C. The waste water is made harmless in this way.