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Costas Karamanlis will spend three days Turkey, but the visit may be more about political symbolism than substance.
A new joint gas pipeline was opened late last year, and trade has boomed, however relations have been strained between the two countries in the past.
In 2005 there was a stand off between Greek and Turkish patrol boats in the Aegean Sea, and in the same year a Greek fighter pilot died when his plane clashed with a Turkish plane in disputed airspace.
There is now a new system of communication between both defence forces.
It is hoped the Greek leader's visit will help the long running dispute over the divided island of Cyprus.
Source: By Australian Broadcasting Corporation