Police are trying to track down the owner of the dog.
It's the second incident in a month - although the first bird survived.
But on Friday, a man's dog killed a black female swan which recently lost her cygnet. Passers-by tried to intervene to protect the bird but she died from her injuries. The cygnet's father also tried to get the dogs off its mate.
Town Clerk Andrew McKenzie says action will be taken place against irresponsible dog owners.
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