An Adelaide woman has been ordered to stand trial for the murder of another woman, whose body was found with up to 40 stab wounds.

Cynthia Ellen Rigney, 19, pleaded not guilty to murder when she appeared in Adelaide Magistrates Court by video link on Tuesday morning.

Later in the day, the court lifted a suppression order on her name that had been in place since her first appearance.

Rigney is accused of stabbing to death the 61-year-old victim in Kilburn, in Adelaide's north, in December last year.

Prosecutors said she was captured on CCTV arriving at the victim's house and the body was found by two people about 30 minutes later.

The victim had between 30 and 40 stab wounds to her upper body, police said.

Chief Magistrate Mary-Louise Hribal remanded Rigney in custody to face the Supreme Court next February.