We have been giving her time out, taking away certain activities she enjoys but it does not seem to be working. Is this a larger behavioral problem or is this just part of an older sibling being jealous of her younger brother.
It depends on what you mean by the word harshly. Should you employ physical discipline? No, you should not. But an immediate time out for any physical aggression is sensible. It won't be sufficient to say 'No biting' without the time out.