The invention is a process for epoxidizing an olefin with hydrogen and oxygen in the presence of a catalyst mixture containing a titanium or vanadium zeolite and a supported catalyst comprising palladium, gold, and an inorganic oxide carrier. Prior to its use in the epoxidation process, the supported catalyst is calcined in the presence of oxygen at a temperature from 450 to 800.degree. C. and reduced in the presence of hydrogen at a temperature greater than 20.degree. C. The process results in significantly reduced alkane byproduct formed by the hydrogenation of olefin.