A catalyst for purifying the exhaust gases of a diesel engine, comprising a support material containing at least one zeolite and, additionally, at least one of the support oxides selected from the group consisting of aluminum oxide, silicon dioxide, titanium dioxide, zirconium dioxide and aluminum silicate and mixed oxides thereof and at least one of the noble metals selected from the group consisting of platinum, palladium, rhodium, iridium, gold and silver, wherein atoms of the noble metals present in said catalyst have a mean oxidation number of less than +2.5, on average more than 3 metal ligands and less than 3 oxygen ligands and are present on the zeolite and support oxides in the form of crystallites having a mean particle size from 1 to 6 nm made by a process wherein said support oxides and the zeolites are first impregnated separately with precursor compounds of the noble metals, and then calcined in the still moist state in the course of from 0.1 to 10 seconds by being blown into combustion waste gases at a temperature of from 500 to 1000° C., and are then processed to a common coating dispersion with which a monolithic honeycomb body is subsequently coated, and the coating is then dried, calcined and, finally, reduced.