A nurse has been charged with the murder of two elderly patients at a nursing home at Ballina in northern New South Wales.

Marie Darragh, 82, and Isobella Spencer, 77, were allegedly given unscheduled doses of insulin in May this year, and died shortly afterwards.

Megan Haine, 46, has also been charged with the assault of a third patient.

It is alleged that woman, aged 88, was assaulted when she found the woman trying to inject her with insulin.

Haines was arrested at Seaspray in eastern Victoria on Monday and extradited to Sydney late on Tuesday.

She has been formally charged with two counts of murder and one of assault.

Haines is being treated for severe depression and did not oppose extradition or apply for bail.

She will front Central Local Court on Wednesday.