A method for improving the selectivity of a supported highly selective epoxidation catalyst comprising silver in a quantity of at most 0.17 g per m.sup.2 surface area of the support, which method comprises contacting the catalyst, or a precursor of the catalyst comprising the silver in cationic form, with a feed comprising oxygen at a catalyst temperature above 250.degree. C. for a duration of up to 150 hours, and subsequently decreasing the catalyst temperature to a value of at most 250.degree. C.; and a process for the epoxidation of an olefin, which process comprises contacting a supported highly selective epoxidation catalyst comprising silver in a quantity of at most 0.17 g per m.sup.2 surface area of the support, or a precursor of the catalyst comprising the silver in cationic form, with a feed comprising oxygen at a catalyst temperature above 250.degree. C. for a duration of up to 150 hours, and subsequently decreasing the catalyst temperature to a value of at most 250.degree. C. and contacting the catalyst with the feed comprising the olefin and oxygen.