The case has gone through a total of 13 pre-trial hearings, Mr Burdes told Christchurch District Court today.
Judge David Holderness said the move to withdraw the charge was ``a sensible decision''.
Cornes still faces a charge of attempting to obtain $18,250 by deception, and will be back in court for a pre-trial hearing later this month.
Cornes, who has denied both charges, declined to comment outside court today.
Police say they spent three years tracking down Cornes - a target they labelled a "ghost''.
They issued airport alerts after learning that he often travelled to Australia where he had reportedly been a leading colonial art dealer in the 1980s.
Cornes was found living in Christchurch early last year and was charged.
He says he has been fighting to clear his name and reputation ever since.