Neth's body was found on February 22 along with seven others that were identified a week ago, said the prefecture in Grosetto, which has jurisdiction over the island where the ship crashed.
Five other bodies were found in the ship's wreckage on Thursday, but it will take divers a few days to recover them before they can be identified.
The Costa Concordia was carrying 4,229 passengers and crew when it struck rocks off Giglio island in Tuscany and keeled over on the night of January 13, killing 32 people. So far 30 bodies have been found but two are still missing.
Meanwhile, salvage workers who began pumping 2,400 tonnes of fuel oil from the ship's tanks on February 12 have finally finished the operation, the Costa Crociere company said.
The company's statement said all the fuel had been pumped out apart from "minor traces impossible to remove from the reservoir walls, (which were) such small quantities that they present no real hazard to the environment."
Italian prosecutors have placed the ship's captain, Francesco Schettino, and first officer, Ciro Ambrosio, under investigation for the disaster.
Dozens of survivors have launched lawsuits against cruise line Costa and its US parent company Carnival in France, Germany and the United States.
Costa has offered uninjured passengers €11,000 ($14,500) each plus expenses as compensation.