Last week, the BBC was forced to apologize to the queen after it showed a promotional trailer for an upcoming RDF-produced documentary that implied the monarch had left the sitting after Leibovitz asked her to remove her crown.
"Clearly RDF has been guilty of a serious error of judgment and I deeply regret the embarrassment this has led to for both the BBC and the queen and wanted to apologize to you unreservedly," Frank wrote.
The BBC released a copy of the message, which was sent to its director-general, Mark Thompson.
Frank condemned the actions of his employees who edited the footage out of sequence and said he was taking steps to ensure it would not happen again.
The trailer released by the BBC to journalists on July 11 showed the queen arriving for the sitting -- not walking out of it, as the sequence implied.
The scene showed the queen walking down a corridor, wearing a crown and her Order of the Garter robes, and telling her lady-in-waiting: "I'm not changing anything. I've had enough dressing like this, thank you very much."
The BBC and RDF apologized to the queen and Leibovitz last week. They said the trailer had never been intended for the public and had been shown to journalists in error.