IS SAUL STILL A LEADER AFTER GOD'S REJECTION

^{1 SAM 15:26} But Samuel said to him, "I will not go back with you. You have rejected the word of the LORD, and the LORD has rejected you as king over Israel!" After God's rejection of King Saul, Saul was still sitting at the throne and the people still recognised him as king. Why isn't his rejection visible to Israel?