A supported catalyst containing rhodium and compounds of chromium, manganese, alkali metals and, if appropriate, compounds of sulphur is prepared by first applying compounds of chromium and manganese to the catalyst support, subsequently heating the catalyst support thus charged to elevated temperatures and then impregnating it with a rhodium solution, drying it, treating it with an alkali metal solution and, if appropriate, applying sulphur compounds to the catalyst support thus treated. The supported catalyst thus prepared can be used for the dehydrogenation of compounds and/or compound mixtures consisting of completely and/or partly hydrogenated hydroxydiphenyl.