Sure - just do a cash advance.
Depending on the terms of your card, you will probably be charged 3% of the cash advance as a fee, and your APR for the $16,000 will be at the cash advance APR (often 24%+).
Perhaps a better idea would be to apply for a 0% balance transfer promotional card. Do some research and make sure you apply for a card that will issue a check for the balance transfer. (say that it is for a personal loan that you are repaying... it is sort-of a personal loan that you took from your own account...). If you can't find a card that will do a BT to your checking account, do the balance transfer to your other credit card which will cause your balance to go to -$16,000 and then ask for a refund check. (check with your credit card company to make sure they will allow your account to go to -$16,000)