As far as I know, Unetbootin should work for Mint 16. Mint 10 is old. You may need to get the latest version of Unetbootin from their website.
Just download the ISO from the website, open Unetbootin, and tick "Diskimage", choose the ISO file you downloaded, make sure it's set to USB drive, and click "OK". Then have a cup of tea, go for a walk, etc. while the distro is installed to your USB drive.
You also may want to check the md5 checksum just to make sure your ISO is intact. To do this, just do:
If, for some reason, Unetbootin does not work, you can try other programs (see http://community.linuxmint.com/tutorial/view/744
) such as PenDrive Linux or mint stick.