A method for the manufacture of an ester by transesterification allows the transesterification reaction to proceed within a short reaction time and under a pressure of the order of normal pressure. It was found that transesterification proceeds when a starting material ester and an alcohol are brought into contact with a catalyst comprising (A) an amorphous zirconium oxide and (B) an oxide of a Group II element, an oxide of a Group V element, and/or an oxide of a Group IV element other than zirconium and hafnium. In this method, it is preferred that the starting material ester in a liquid-phase state and the alcohol in a vapor-phase state be brought into contact with a solid acid catalyst comprising the above components (A) and (B), the starting material ester be an oil or fat, and the alcohol be methanol or ethanol. An oxide of titanium, silicon, germanium, or tin is the preferred oxide of the Group IV element other than zirconium and hafnium.