The only part of the missing Boeing 777, which vanished two years ago with 239 passengers and crew on board, that has so far been found and officially identified was on the French island of La Reunion.
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The same man who discovered that "flaperon" part last July while cleaning a beach found the second object measuring about 40 by 20 centimetres (15 by eight inches) in early March.
Australia's Joint Agency Coordination Centre (JACC) is running the search in the southern Indian Ocean, where the jet is believed to have diverted to from a Kuala Lumpur-Beijing flight path.
The centre said Malaysian officials were "continuing discussions with French authorities about debris found on La Reunion".
But they added in a statement that "current advice is that it is unlikely to be from an aircraft".
JACC said arrangements were being made for two other suspected pieces of MH370 debris found in Mozambique in recent weeks to be brought to Australia's capital Canberra.
The two items will be examined by investigators from Australia, Malaysia and Boeing at Australian Transport Safety Bureau's laboratories "to confirm if they come from an aircraft and establish their origin".
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The hunt for MH370 is expected to wrap up around June to July if the aircraft is not found in the target zone of 120,000 square kilometres (46,000 square miles).
No crash site has been located, but Australian authorities told AFP ahead of the March 8 two-year anniversary of the plane's disappearance they were still hopeful it will be found.
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