Snap Without Using Your Thumb

Snap faster, louder, and more precisely without using your thumbs for support. Guaranteed to draw attention.

Steps

Position your ring finger in the same position as you would snap normally. To find this spot, snap normally and keep the finger in the exact spot it is when the middle finger lands on it.
Raise your index and middle fingers up until they're at a ninety degree angle with the back of your hand.
Push your finger as quickly as possible down so that it lands half on and half off of the ring finger, which should not have changed position. This is the same spot it should land when snapping regularly, and, if performed hard enough, will make the sound.

Push down hard with the ring finger to keep it in the same position.
It doesn't matter how you handle your index and little fingers, just keep them out of the way.
This trick takes serious strength of the fingers, so practice often. Other things with the fingers, such as tapping on tables and playing musical instruments, can help build the required strength.
This technique allows you to snap fast enough to make recognizable and impressively fast beats, so practice faster and try snapping to different beats.
Use both hands alternating to double your speed.
The thumb should be bent in the same way it is bent after completing a normal snap.
Speed is very important, and so is practicing!

If your fingers aren't very strong, do not practice too much. The finger muscles are very small, and you don't want to tear or damage them from overuse. This risk is exacerbated if your hands are cold.
Be careful who sees you do this! Some cultures consider it inappropriate.