Batter throwing bat

[canadaump6]

How do you guys deal with a batter who tosses his bat after making contact with the ball? Do you eject the unsafe player immediately, or give him a warning? My procedure has been to wait till the inning is over, then write the offending player's number on my lineup card, and tell the coach "player number xx is getting his warning for throwing the bat". If he does it again, player is ejected.

I had a coach challenge my way of handling this situation, who stated that there was no rule about not throwing the bat. I feel rule 9.01a is sufficient to cover the handling of an unsafe player- part of the umpire's job is to maintain order and discipline on the field.