The father-son succession continued until Kinkuni HASHIMOTO, the sixth generation, who did not produce an heir, at which point Kinnatsu HASHIMOTO (1454-1538) was adopted from the Shimizudani family of the same Saionji clan.
6代目の橋本公国まで父子相続が続いたが、公国に跡継ぎがなく、同じ西園寺家一門の清水谷家から橋本公夏（1454年－1538年）が養子に入った。