16 month old bites herself when shes mad?

My daughter, naturally, started the tantrums when she turned 1. We don't spank, but we do (attempt) to use time-outs in the corner. When she gets angry, she started hitting people and biting people! Mostly us of course.. but if she got mad at someone else, she'd do it to them, too. After several stern "NO's!" she has cut the hitting down to pretty much a rare thing. But NOW, when she gets upset, she bites HERSELF! She will bite her arm so hard, she leaves teeth marks. She is my first child, so I dont know if this happens to anyone else.. but to me and some others, it seems really unusual....I feel especially since we use no form of spanking/physical fighting or anything like that in our house?