A method for the production of a catalyst, which comprises depositing silver and an alkali metal on a carrier containing 90.0-98.9 mass % of α-alumina, 0.01-1 mass % of a compound of at least one metal element selected from the group consisting of potassium and iron (calculated as oxide), 0.1-5 mass % of a silicon compound (calculated as oxide), and 1-5 mass % of zirconium compound (calculated as oxide), drying the resultant composite, heat-treating the dried composite at a temperature in the range of 60°-450° C. in the presence of an oxygen-containing gas, and subjecting the heated composite to a high-temperature heat treatment in the atmosphere of an inert gas at a temperature in the range of 450°-700° C.