The family of a murdered Greek-Australian man say they are not giving up after a court in Greece rejected the extradition of James Dalamangas to Australia.

Greece has ruled out sending James Dalamangas back to Sydney to face a court, decades after a fatal nightclub stabbing.

A Greek appeals court this week ruled that a 56-year-old man wanted by Australia on a homicide charge will not be extradited, his lawyer said.