Kara DioGuardi, the songwriter who was added as a fourth judge on “American Idol” last season, will return to the Fox reality show next season, the producers of the show announced Monday. That leaves the fate of Paula Abdul as the only unknown factor in the lineup of four judges and one host as the show prepares for the first appearance, later this month, of potential contestants for the show’s ninth season before the judging panel.

Ms. Abdul’s contract expired at the end of last season, and she has been negotiating, so far unsuccessfully, with the producers for a substantial raise from the estimated $2 million that she earned last year.

This summer, Ryan Seacrest, the show’s host, signed a deal that promises him $45 million over the next three seasons. Simon Cowell, who earns an estimated $30 million a year as a judge and has the right to sign management contracts with “Idol” contestants, and another judge, Randy Jackson, are under contract through next season.

Ms. Abdul has said she wants to return to the show, and Fox Broadcasting and the show’s producers have said they want her back. Ms. Abdul has recently commented on the negotiations on her Twitter account, saying last week, “I hope you can understand I can only return to Idol if the deal is fair.” Edward Wyatt