When you say normal sim, I assume you mean the mini-sim. Normal (standard size) sim being the size of a credit card.
The iPhone 4 uses a micro-sim, but this does come on a standard size Sim card. In fact you have to snap the micro-sim out of the mini-sim which can in turn be snapped out of the standard sim.
Don't snap the micro-sim out of the mini-sim in the first place, or if you can't avoid that then there are adapters that will allow you to put a micro-sim into a phone that takes a mini-sim.