President Napolitano put the returned fragment in place in 2008.
A piece of the Parthenon temple frieze which was returned to Greece by the Italian government has been sent back to Italy again.
Putting the piece on show in Athens in 2008, Italy's president said the return was part of a campaign to restore artefacts "torn from their context".
Some reports implied pressure on the British Museum to return its collection of Parthenon sculptures would increase.
But the fragment has now gone back to a museum in Palermo, Sicily.
The fragment of a goddess's leg, measuring 34x35cm, had been on show in the Acropolis Museum, designed to reunite all the surviving sculptures from the Parthenon temple.
It had been in Sicily since it was donated to Palermo University by the widow of a British diplomat in 1836.
In September 2008 it went on show in Athens at a ceremony attended by Italian President Giorgio Napolitano.
But its return to Italy was arranged following the expiry of the loan, say Italian officials. Regional cultural director Gaetano Armato said a long-term loan was possible in future, following the signing of a cultural "reciprocity agreement" by the British government and others.
The fragment is one of a number of small pieces of sculpture which have been returned to Greece in recent years: a man's heel from Germany in 2006; a piece of the neighbouring Erechtheion temple from Sweden the same year; and the head of a youth from the Vatican in November 2008.
The fragment (left) is part of a goddess's leg.
The Greek authorities want to combine their own Parthenon sculptures with those from the British Museum and a number of smaller pieces which are scattered in museums across Europe.
But the British Museum says the sculptures it holds are "an important part of a world collection which is free to all and which allows six million visitors a year to explore the complex network of interconnected world cultures".
After the Palermo fragment was sent back to Sicily, Prof Tony Snodgrass of the British Committee for the Unification of the Parthenon Marbles said: "The museum at Palermo was very much the hardest to persuade to lend.
"The transfer was always officially said to be 'temporary', as is also true of the pieces from the Vatican, but it wasn't clear whether this would be strictly enforced.
"It may happen in due course with the Vatican too, but not necessarily."