The health authorities in French Polynesia now say a 24-year-old woman who died on Wednesday was the victim of swine flu.
In a statement, they say she was considered to be an at-risk patient because of her medical history.
The health minister has assured the public that in itself, the flu won't
kill, but can be fatal for some with underlying health problems.
53 people have contracted swine flu in the territory, with eight of them now in hospital.
One of them is in a serious condition.