Just purchased a 2005 elantra & the manual says that when you arm the alarm with the transmitter, you can use transmitter or a key to unarm. Whenever I unlock with the key, the alarm goes off. Am I doing something wrong here??

No, it's an error in the manual. If you've armed it using the key fob, you MUST use the key fob to disarm it.

In the U.S., all Elantras come with the keyless alarm system I think. But in other markets, they don't have the keyless but still have an alarm (which is activated by locking the doors with the key). So what the manual should say is: If the car was locked with the key, unlock it with the key. If it was locked with the fob, unlock it with the fob. I actually spoke to someone at Hyundai USA and he confirmed it is an error in the manual.

Thanks for the reply. I don't like it this way, but guess I'll have to get used to it!

Yep.

I just bought a 1998 Mercury Tracer for my son to drive. It has an alarm system as well. If you set it, then use the key to unlock the door, the alarm goes off, but as soon as you put the key into the ignition and turn it, the alarm shuts back off. Which is good because we only got one key fob, and if we lost that (which is inevitable with an 18 year old), we'd be screwed.