Despite her last-minute effort, billionaire Gina Rinehart lost her bid to keep secret the family's legal battle over its $10-billion wealth.

On Monday, New South Wales Court of Appeals Chief Justice Tom Bathurst declared a previous suppression order was not in line with open justice due to the alleged misconduct and breach of trust by Ms Rinehart. The appeal was filed by Fairfax Media, publisher of the Sydney Morning Herald and The Canberra Times, and other media,

The decision prompted Ms Rinehart to file with Justice Margaret Beazley to seek a stay of the decision to enable her to apply to the High Court a leave to appeal. However, Ms Beazley withheld her judgment until Wednesday.

Her two daughters and son - Hope Rinehart Welker, Bianca Hope Rinehart and John Langley Hancock - sought to have Ms Rinehart removed as head of the family trust set up by her father, mining magnate Lang Hancock, due to her alleged misconduct. A fourth child, Gina Hope Frances Rinehart, supports her mother in the family legal battle.

Since the start of the lawsuit, the case has been suppressed. The court had sent out order that stopped the publication of information and evidence in the legal proceedings. Media organisations challenged the suppression orders.