The breakdown of the alumina RF-windows used in high-power klystrons is one of the most serious problems in the development of klystrons. This breakdown results from excess heating of alumina due to multipactor bombardment and/or localized RF dissipation. In order to develop RF windows having high durability for the KEKB klystrons, several kinds of alumina ceramics are being examined, and the breakdown mechanism of RF windows are being considered. An improved RF window installed in a KEKB klystron is also being tested.