Later, Yoritomo himself was designated for seii taishogun (literally, "great general who subdues the barbarians"), followed by his sons, MINAMOTO no Yoriie and MINAMOTO no Sanetomo, establishing the system of making the post of seii taishogun hereditary.
後に、頼朝自身が征夷大将軍に就任し、彼の子である源頼家・源実朝が就任したことで、征夷大将軍の世襲がおこなわれるようになった。