Stand in the right pec position with your elbow facing your target with nothing in your hand. Keep your wrist limp and let your hand hang towards your chest (fingers and thumb pointing towards your chest, hanging down a little.) It's ok to be pointing at your sternum instead of your right pec. Using your shoulder and your elbow, jab your elbow forward like you're trying to elbow something in front of you. You should feel your hand collapse into your forearm and bounce. Play with your elbow height and using different muscles to perform this until you feel the one that gets you the most bounce. Now, when you feel your hand collapse, chop your forearm open and you can feel your wrist swing open. That's the feeling you're looking for, your wrist will swing from closed to neutral (or open) instead of neutral to open, which is what the towel whipping motion does. Start reaching back a little and see if you can keep that feeling. Keep going back and working with it until you're able to work it into your throw. Like Blake said, anything that makes that feeling better, keep with it. Anything that causes you to lose it, get rid of it. Many people have posted little tips and hints, those will help you more if you know what feeling you're looking for to begin with.
I could be doing something completely different when I actually throw, so someone correct me if I'm wrong. But that's how I initially got out of the rut of the wrong snapping motion.