Federal Indigenous Affairs Minister Amanda Vanstone says the Government will consider appealing against a Federal Court decision which found ATSIC chairman Geoff Clark was wrongly suspended.

Mr Clark was removed from the position after he was convicted of obstructing police during a pub brawl, but he has won an appeal against the decision.

Senator Vanstone says she is still considering the Federal Court ruling but an appeal is an option.

She says she stands by her original decision.

"The decision to suspend him had to go before both houses of Parliament to see if they agreed and neither house rejected those motions," she said.

"I'm aware of the Federal Court decision, I think it's a shame but in a sense let me put it this way, Labor wants to get rid of ATSIC, they say they do, we've got a bill to get rid of ATSIC, let's get on and do it, let's get rid of ATSIC, it's irrelevant."