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Both toddlers were rushed to hospital by their parents on Sunday after they were swooped by the same male native bird a few hours apart at Whiteman Park in Perth's north.
One-year-old Jacob Gale underwent emergency surgery on his left eye after the bird punctured his eyeball with its beak.
"They've had to remove the lens of the eye because it's damaged," Jacob's father Adam Gale told Channel 7 News.
Until Jacob can communicate, doctors won't know if his son has suffered long-term sight damage, he said.
Despite being swooped twice, three-year-old Bodee White suffered no permanent damage from scratches inflicted to his face and eyeball.
Both Bodee's mother Rebecca White and Jacob's family said they did not want the magpie destroyed.
However a Department of Planning spokeswoman told AAP the bird was "euthanised humanely" on Wednesday.
"It posed a clear danger to the public and was positively identified as the dangerous bird."
She said staff and multiple signs spread across Whiteman Park warned the public to beware of swooping magpies during breeding season from August to October.
Magpies are a protected species and wildlife officers were issued a license by the Department of Biodiversity, Conservation and Attractions to exterminate the bird.
A Brisbane-based study found only 10 per cent of magpies actually swoop to protect their newborn chicks and are unlikely to attack people who feed them.
It is recommended people wear hats and sunglasses for protection or avoid areas prone to swooping magpies entirely.