Penwith District Council has decided that thesternboard from the HMS Association, which was wrecked near the Islands in 1707, should remain in Penzance.
The vote confirmed a decision by Penzance Town Council in July not to return the artefact to the Islands.
In April, the Policy and Resources Committee of the Islands’ Council had resolved by 6 votes to 1 that the sternboard - currently in Penzance Magistrates’ Court - should be displayed in the council chamber as part of a commemoration of the 300th anniversary of the disaster later this year.
The latest decision was welcomed by Cllr Gordon Bilsborough, who had argued that retrieving the sternboard would cost the average Scilly taxpayer £20 per head.
He said: “I am delighted that common sense has prevailed. There was a real danger that the sternboard could have fallen to pieces when being removed from the wall in Penzance.
“But more importantly, it means that it will save council tax payers on the Isles of Scilly £20,000 which had been allocated from our dwindling reserves. We have far more important priorities to deal with.”