Harold Hamm and ex-wife Sue Ann Arnall are fighting over his fortune. Picture: AP Source: Supplied

But that’s just what ex-wife of oil driller Harold Hamm did on Tuesday.

Sue Ann Arnall, formerly Sue Ann Hamm, turned down an offer for $US 974.8 million ($AU 1.2 billion) to settle the couple’s bitter divorce, Reuters reports.

The money was awarded to Arnall in a November divorce ruling by an Oklahoma County judge but her lawyers said she was appealing that decision and holding out for more.

Her lawyers had previously contended her award is inadequate given the couple’s 26-year marriage. They say she deserves closer to $US 18 billion.

“We are seeking clarification of the court’s November 10 order at today’s hearing and cannot accept any payments ... without jeopardising Ms Arnall’s rights on appeal,” Arnall’s lawyer Ron Barber said.

Mr Hamm, 68, was an early believer in the Bakken oil shale formation, which is spurring the oil boom in western North Dakota — now the United State’s second largest oil producer behind Texas.

He owns 60 per cent of stocks in his company — Continental Resources — and more oil than any other American.

But Mrs Arnall is no lady of leisure. She is a lawyer and an economist and has worked at her husband’s oil firm at various times in their marriage, at one point managing the marketing department, according to court documents.

There were fears that Mr Hamm could lose control of the company in the split from his second wife with no prenup in place.