To remove the nitrogen oxides from the exhaust gas from lean-burn engines, these engines are equipped with a nitrogen oxide storage catalyst, which has to be regenerated frequently by the engine being briefly switched to rich-burn mode. The regeneration is usually initiated when the nitrogen oxide concentration downstream of the catalyst rises above a permissible value. In this context, there is a risk of the bed temperature of the catalyst during and after regeneration being pushed into a range with incipient thermal desorption of the nitrogen oxides on account of the heat which is released during the conversion of the nitrogen oxides by the reducing constituents of the exhaust gas. This can lead to increased nitrogen oxide emission both during the regeneration itself and after the engine has been switched back to lean-burn mode. To eliminate this problem, it is proposed to divide the rich-burn mode into two rich pulses which follow one another in time, the first rich pulse being of shorter duration than the second rich pulse.