By Joia Shillingford BBC News business reporter

Martha Stewart on her ranch

She has already served five months in jail for her role in a share scandal, and was released earlier this month to start her five-month house arrest term.

But she claims her sentence is unconstitutional and on Thursday asked the US Court of Appeals for the 2nd Circuit to resentence her.

This would give the judge the option of shortening her sentence, says the Washington Post, which reported the story.

Ms Stewart lives on a large ranch just 40 minutes outside New York, but is only allowed out to pursue gainful employment for 48 hours a week.

Tight timetable

As a result the billionaire homemaker, who recently made it in to the Forbes rich list, is probably finding she's hard pressed for time as her work commitments include several TV shows, as well as providing creative input to Martha Stewart Living Omnimedia - her publishing-to-homewares empire.

Now CBS is going into production on a TV film about the last six years of her life, with actress Cybill Shepherd, tipped to play Martha.

Ms Stewart's last six years could be seen on television in a CBS film

No doubt this will involve lucrative consultancy fees for Ms Stewart. After all, someone has to tell CBS what it was like for her in prison.

Ms Stewart has also complained that the electronic ankle tag she has to wear is rather uncomfortable.

In an online chat with some of her many fans earlier this week, she described the tag with transmitter that beams her location to the law enforcement services as "rigid" and "somewhat uncomfortable and irritating".

Appeal bid

Her lawyer is arguing that her conviction should be reversed on several grounds: that one juror lied on his screening questionnaire, that a government witness perjured himself, and that she was not allowed to cross-examine her former broker in court.

Another factor is that a new Supreme Court ruling has found that mandatory federal sentencing guidelines are unconstitutional. Since that decision, federal sentencing guidelines are regarded as purely advisory, which means Ms Stewart could be given a more lenient term.

Ms Stewart and her former broker Peter Bacanovic, were convicted of conspiracy and lying to authorities over Ms Stewart's sale of shares in drug company ImClone, shortly before its cancer drug ran into regulatory trouble.

Never one to compromise on her appearance, Ms Stewart wore trousers to the court, which made it impossible to see the ankle tag.