Kate Middleton and Meghan Markle may have had some tense moments together. Royal author Tom Quinn details an incident that left the Duchess of Cambridge "really upset" after the Duchess of Sussex criticised one of the members of Kensington Palace staff.

In his new book titled "Kensington Palace: An Intimate Memoir from Queen Mary to Meghan Markle," Tom Quinn provides details of an alleged heated incident between the two duchesses. According to Daily Star, he claims to have spoken to Kensington Palace insiders about the relationship between the wives of the royal brothers Prince William and Prince Harry.

According to the report, Meghan Markle felt she was not "being treated with the same respect as Kate" during her time as a member of the British royal family and when they were living in Nottingham Cottage in the grounds of Kensington Palace. Since her cottage was smaller than the Cambridge family's Apartment 1A, Meghan felt like she was some sort of a "runner-up."

"Meghan and Harry were living in what's called Nottingham Cottage and it's probably the only bit that you genuinely really could say, is actually quite small," Quinn said. "And so I think that reminded Meghan that she was, as it were, second place or as the runner-up."

The author also recalls an incident when Meghan allegedly "lost her temper with a member of Kate's staff in front of Kate." This happened on one of the occasions when the four royals got together.

The royal author reveals more details that he claims to have received by someone who was present at the moment when this "foot-stamping" incident took place.

"The reason she lost it with Kate's member of staff was that she, Meghan, didn't feel that this person was giving her the sort of attention she deserved. It was almost as if in that one encounter, it encapsulated for Meghan the problem that she had, that she's a Princess and she's number two," Quinn explains.

He goes on to say that it was described to him in a way there were "raised voices and foot-stamping." This encounter left Kate "horrified" and "really upset" particularly because the mother-of-three is "very fond" of this staff member.

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Princess Beatrice, Princess Eugenie, Princess Anne, Princess Royal, Prince Andrew, Duke of York, Prince William, Duke of Cambridge, Catherine, Duchess of Cambridge, Meghan Markle and Prince Harry attend Christmas Day Church service at Church of St Mary Magdalene on 25 December 2017 in King's Lynn, England. Chris Jackson/Getty Images

Quinn claims that the insiders revealed that Kensington Palace staff member refused to fulfil Meghan's wish because she worked for Kate. Later, however, Meghan and Harry moved to Frogmore Cottage, and soon after, they quit the royal family. They are currently residing in LA with their one-year-old son Archie.