But Mr Burdett accepted that if the court finds the conviction was sound, then "that is pretty much the end of the matter".
"I have no issue with the police on this. There were a series of events that unfolded ... and it's all very well to look back with hindsight, but I am more interested in looking forward," he said.
"I'm not looking for vengeance ... I like to see justice and I like to see truth.
"While I would like to see a resolution to this, I can fully accept things. I'm not holding my breath."
Over the years, Mr Burdett said he had managed to cope with his sister's death and the ongoing, high-profile case.
"Life throws a lot of stuff at you, both good and bad. You accept it and you eventually integrate it into your personality and who you are. One of the facets of who I am is a brother whose sister was murdered. And once you get that sense of acceptance and integration, the anger and the hurt recedes quite a lot. I dealt with that a long time ago."