Biting, headbanging, tantrums, going mad Help!

[dalieo]

My 2.5 ds keeps biting his sister (1.5) doesn't bite anyone else just her really hard. Marks all up her arms. Confesses his crimes once he has done it doesn't show any remorse, but knows that it is naughty behaviour.
Has also started (in the middle of one now) having massive tantrums banging his head against the stairgate hard. Never seen anything like it. Anyone out there similar exp/suggestions. I feel like I'm going mad!!!!

Just wondering, is your ds maybe jealous of his lil sister? Or does he do it at certain times, i.e. maybe she is invading his space or trys to play with his toys or somehting like that?
The Tantrum sounds bad...he is of course just the right age for those, but banging his head on the staircase..ouch...saying that my es used to throw himself on the floor and then bang his head on the floor over and over....
sorry, have no suggestions on this...