According to "Nihon shoki" (the Chronicles of Japan) and "Shoku Nihongi" (Chronicle of Japan Continued), there were some cases in which the post of Sadaijin also became vacant if there was no one qualified for Daijokan in the early Ritsuryo System.
『日本書紀』『続日本紀』などの記録を見ると、律令制の初期には条件を満たす太政官が存在しない場合、左大臣も空位になっていたケースが存在した。