The interim secretary general of Formula 1 is no longer with the governing body.
The statement said that Rao had joined to help the new president.
She was leaving due to the end of the period.
According to senior sources, she resigned because she didn't like the job she was given.
"Shaila-Ann has provided me with great support in respect to Formula 1, always acting with professionalism and integrity."
As special adviser to Mercedes F1 team principal, she worked for the FIA.
Her links to Mercedes made them worry.
Red Bull asked if they had been targeted at the height of the cost-cap row.
After Max Verstappen won his second world title at the Japanese Grand Prix, Christian Horner said that he was told that Red Bull was in violation of the financial regulations.
Red Bull exceeded the cost cap by over one million dollars. They were fined $7m and had their allowed aerodynamic research allowance reduced.
At last weekend's Abu Dhabi Grand Prix, a question was posed to Sulayem. She is the interim secretary general according to him. I don't know what interim means.
He said that he sees her intelligence on big decisions. My people will be defended.
There was an allegation that Shaila-Ann is a supporter of Mercedes.
She said that it was a bit harsh. I said, "My God, there is someone accusing her of being with Mercedes and she's saying to me that it's cruel."