The analysis was carried out after initial routine tests for the disease proved inconclusive, sparking concern there may be new cases.
A Defra spokeswoman said: "We have had final negative results on both of them."
Bluetongue was first confirmed in the UK on September 28 in East Anglia. All other cases have been confined to the south east.
The virus, which can be fatal to sheep and cattle, is spread by midges.
Last month the Government relaxed movement restrictions established after the virus was discovered in the UK, saying there was currently a low risk of disease due to falling temperatures and a low midge count.
But with many farmers carrying out testing on their animals before moving them, more suspect cases may emerge which will need further investigation, Defra said.
Tweet

Pippa, Manchester (28/01/2008 at 20:46)