In order to achieve a high degree of conversion, oxides of nitrogen are contacted with a catalyst containing an aluminum silicate having a three-sheet structure as a catalytically active component at a temperature between 100.degree. C. and 700.degree. C. With this type of catalyst, the decomposition of the oxides of nitrogen proceeds without the presence of a reducing agent. Additionally, the degree of decomposition for the oxides of nitrogen is not adversely affected by the oxygen present in the flue gas. Degrees of decomposition greater than 60% were achieved with this catalyst in the temperature range between 200.degree. C. and 600.degree. C. The catalysts of the invention can replace the previous catalysts, which use a reducing agent, for decreasing the amount of oxides of nitrogen in waste gases, for example in flue gas and exhaust gas purification in power stations and combustion engines, respectively.