Earlier this year Europe's horsemeat scandal revealed how processed meat can get mislabelled in a complicated supply chain.
Waitrose also withdrew a number of products when the horsemeat scandal came to light.
The two horsemeat-free samples were found to have pig DNA at below the 1% threshold.
The supermarket said it was the fourth of its products to test positive for horsemeat contamination.
Traces of horsemeat have been found in numerous processed beef frozen meals across Europe.
BBC: Horsemeat scandal: Dutch uncover large-scale meat fraud
New tests have cleared a Powys company suspected of supplying beef burgers containing horsemeat.
Scottish Liberal Democrat rural affairs spokesman Tavish Scott said the horsemeat scandal was completely unacceptable.
The product made on the firm's premises outside Bleary has been found to contain horsemeat.
But it has been sorely tested by the horsemeat scandal, which broke last month.
It was not until January that a decision was made to test it for horsemeat.
Ireland has called a meeting of EU officials from countries affected by the horsemeat scandal.
So then, where are these suppliers, and where are they getting the horsemeat from?
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Minister of Agriculture Daniel Constantin said there is no evidence false horsemeat labeling occurred in Romania.
On Friday, it emerged beefburgers containing horsemeat had been withdrawn from hospitals in Northern Ireland.
The French government has accused meat processing company Spanghero of knowingly selling horsemeat labelled as beef.
Last month, Irish authorities discovered horsemeat in some burgers stocked by some UK supermarket chains.
BBC: Burgers recalled from NI schools are 'clear of horse DNA'
On Wednesday, DUP MEP Diane Dodds described the horsemeat scandal as one of "mammoth proportions".
BBC: Burgers recalled from NI schools are 'clear of horse DNA'
France produces roughly what it consumes in the way of horsemeat (18, 000 tonnes a year).
However, other products have had very high percentages of horsemeat, which is a much larger problem.
On a lighter note, the scandal has inspired a surprise revival for horsemeat in France!
Romania has denied claims that it was to blame for the mislabelling of horsemeat.
Horsemeat has now been confirmed in some frozen lasagne on sale in France too.
Horsemeat is considered a traditional delicacy in Russia and is available in many restaurants and stores.
Russian officials say horsemeat has been found in sausages advertised as pork and imported from Austria.
The French government has suspended Spanghero's licence, saying it "knowingly" sold horsemeat as beef.
Separately, tests will be conducted for possible residues in horsemeat of phenylbutazone, also known as "bute".
It has emerged that some beefburgers on sale in UK and Irish Republic supermarkets contained horsemeat.
Two other German companies, Dreistem-Konserven and Vossko, have been accused of manufacturing products containing horsemeat.
French meat processing company Spanghero knowingly sold horsemeat labelled as beef, the French government has said.
Last week France suspended Spanghero's licence, accusing the firm of knowingly selling horsemeat labelled as beef.
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