To produce an exhaust gas cleaning catalyst which is capable of cleaning nitrogen oxides with methane as a reducing agent and the activity of which can stably be maintained over a long period even in the presence of a catalyst activity inhibitor such as steam.

This cleaning catalyst is prepared by depositing rhodium on sulfato-zirconia. This cleaning process involves decomposing nitrogen oxides in an excess-oxygen-containing atmosphere, in the presence of methane by using the catalyst.