The present invention relates to a process for purifying a gas mixture G-0 comprising dinitrogen monoxide, at least comprising the absorption of the gas mixture G-0 in an organic solvent, subsequent desorption of a gas mixture G-1 from the laden organic solvent, absorption of the gas mixture G-1 in water and subsequent desorption of a gas mixture G-2 from the laden water, and also to the use of a purified gas mixture which comprises dinitrogen monoxide and is obtainable by such a process as an oxidizing agent for olefins.