hydrocarbons abbreviated to u201c hc u201d and carbon monoxide co and simultaneously deoxidizes nitrogen oxides no x such a catalyst is called a u201c ternary catalyst u201d the air fuel ratio needs to be held at or near the stoichiometric ratio in order that the oxidizing and deoxidizing reactions based on the ternary catalyst may be effected at the same time in turn the air fuel ratio feedback control needs to be precisely executed for keeping the stoichiometric ratio a secondary air system 6 introduces air into an exhaust pipe 100 by means of a pump 60 in the operating condition of the engine 1 for example at the start of the engine 1 as requires the establishment of a state in which the mixture contains the fuel in excess of the stoichiometric ratio that is the mixture is u201c rich u201d thus the secondary air system 6 functions to burn and decrease the surplus hc emitted into the exhaust pipe 100 although not clearly seen from the drawing the pump 60 is constructed so as to be operable in association with the air fuel ratio feedback control means 3 etc as illustrated in fig1 the diagnostic equipment of this embodiment is constructed comprising misfire detection means 9 secondary air system failure detection means 10 catalyst deterioration index calculation means 11 catalyst deterioration decision means 12 catalyst deterioration index correction means 13 and catalyst deterioration decision interruption means 14 the.