The Queens Counsel, a vocal critic of the Howard government's treatment of asylum seekers said a Bill of Rights would go a long way.
"A Bill of Rights would certainly provide some ability to prevent the excesses that we saw in the details of what went on in detention centres during the Howard years," Mr Burnside told
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Network Ten on Sunday.
"It would have prevented the decision in a famous case in 2004, which said that a man who has not committed any offence, but who couldn't be removed because he's stateless, the High Court ordered he could be held in detention for the rest of his life."
The United Nations human rights convention could be strengthened and should include climate refugees, Mr Burnside said.
"When a Pacific Island is disappearing beneath the water, to say that those people will have to swim somewhere else seems to me pretty heartless."
Prime Minister Julia Gillard said Mr Burnside was wrong to label people against asylum seekers as rednecks, when she unveiled her new asylum seeker strategy.
"I don't happen to think people are rednecks just because they have concerns about boat arrivals," Mr Burnside said.
"I call people rednecks who advocate shooting them out of the water or turning them back at gunpoint and a lot of these people write to me and tell me that's what they'd do."
Mr Burnside cautiously backed Ms Gillard's plan to create a regional processing centre last week, saying it had been used effectively under Malcolm Fraser.
"(The Fraser government) They organised a regional processing arrangement, about 25,000 Vietnamese boat people each year processed through that system were then brought onshore to Australia and interestingly, even with 25,000 Vietnamese a year, the public were unconcerned."
