(CNN) -- Oscar Pistorius was back in court Tuesday where a judge granted him bail.
Judge Aubrey Ledwaba said Pistorius has proved he is not a flight risk.
Last week, South Africa's Supreme Court of Appeal overturned Pistorius' conviction of culpable homicide and found him guilty of murdering his girlfriend, Reeva Steenkamp.
His lawyers say they will appeal that decision to the Constitutional Court and that Pistorius should be allowed to remain free on bail while they do so.
The hearing before the Constitutional Court could take months.
At the hearing Tuesday, the prosecution said Pistorius may flee to Italy or Mozambique.
"We feel strongly about the fact that he needs monitoring, and should not leave the house at any time," state prosecutor Gerri Nel said.
In October, Pistorius was allowed to move from prison, where he served a year of his original five-year sentence, to house detention.
Pistorius' lawyer Barry Rioux said the athlete was not a flight risk.
Murder conviction
Pistorius shot girlfriend Reeva Steenkamp, a model, four times through a locked toilet door on Valentine's Day 2013, saying he mistook her for an intruder.
On Thursday, Judge Eric Leach ruled the original court judgment had been "fundamentally flawed."
Paralympic gold medalist should have foreseen that his firing of a gun would have killed whoever was behind the door in his bathroom, regardless of whether he thought it was Steenkamp or an intruder.
Prosecutors had argued that the 29-year old -- known as the "Blade Runner" in a reference to the prosthetic legs he uses when he races -- intentionally killed Steenkamp following an argument.
Leach said that although Pistorius had genuine beliefs his life was in danger, he should have acted more rationally.
He never fired a warning shot and shot not once but four times.
"The identity of victim is irrelevant to his guilt," he said.
His jail term hasn't been decided, but he faces up to 15 years in prison.
Double jeopardy?
CNN legal analyst Kelly Phelps said that double jeopardy -- a defense that prevents a criminal defendant from being retried on the same charges following a verdict -- did not technically apply in the Pistorius case for two reasons.
The first was that Pistorius wasn't completely acquitted on the original charge but had been convicted of culpable homicide.
"Strictly speaking, because murder wasn't a separate charge but was tied in with the culpable homicide charge, it's not considered technically ... as reconsidering a case where there has been a complete acquittal," said Phelps, a senior lecturer in law at the University of Cape Town.
The second reason, she said, was that the appeal "was based on a question of law, not a question of fact."
"The argument is that where there's been a mistake in law that's been made -- that is the only reason that an incorrect verdict has been reached -- it would be offensive to the interests of justice in order to allow that verdict to stand," she said.
CNN's David McKenzie and Brian Walker contributed to this report.
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