I bought all the season's and Kono had her badge taken away for the same reason Chin did. He was under investigation for taking money, he was cleared because he didn't take it. Their uncle did but Chin wouldn't tell on him so the Governor stated investigating Kono. She Lost her badge & decided to go on the run with Adam Moshamorie (can't spell it) so now that Adam is gone & she found out he is still alive, she's going to try to find him because she fell in l’amour with him. That's why Steve hired Catherine Rollins (his girlfriend) to be a part of Five-0.
