Sometimes it is best to ignore sibling rivalry. But if the stakes become too high, or the squabbling goes on for prolonged periods of time, there are things you can do. Send them to different rooms where they can no longer see each other until they calm down. I'll sometimes act like I'm refereeing a ball game and call a time-out. After they go to their own rooms for awhile they cool off, and the problem is either resolved or forgotten.
Empty threats have no power.
Discussion and reasoning will work with some teens, but only after they've had a chance to calm down. If you choose this method, remember to be impartial and intervene only as a moderator. There are as many different reasons for sibling rivalry as there are teenagers. What works for one family may not be the right for another. And don't be afraid to choose counseling as an option for your family.