The death of Queen Elizabeth II in September brought the royal family back together in mourning but it allegedly also made strained relationships between Meghan Markle and Kate Middleton worse.

The Queen's funeral was the most time that the Duke and Duchess of Sussex spent with the royals, especially with Prince William and Kate Middleton. They reunited for a walkabout outside Windsor Castle on Sept. 10 and participated in most of the events including the vigil at Westminster Abbey and the state funeral on Sept. 19.

There was a temporary truce as the family paid their final respects to Queen Elizabeth II. But returning to the U.K. has reportedly only fuelled the rivalry between Meghan Markle and the new Princess of Wales.

"Coming face-to-face last month has further ignited the rivalry between Meghan and Kate, rather than relieving tensions," a source told Closer magazine in its Oct. 19 issue.

The insider added that the unexpected reunion prompted the former "Suits" star to be "on an all-out mission to get one up" on her sister-in-law. The tipster likened the alleged rivalry "to a game of chess with Meghan trying to outdo Kate every time she makes a move and intentionally making her own move in a bid to get one-up and undermine her."

"Meghan's always felt like she's been in Kate's shadow and being back in the UK recently, she felt that more than ever, so it reignited her drive to win and come out on top," the source further told the publication, adding that the Duchess of Sussex has been making subtle "secret messages" to tell her sister-in-law that "she'll never back down."

This allegedly includes the reported move from Montecito to the elite Hope Ranch neighbourhood. The unnamed insider claimed that Prince Harry and Meghan Markle's plan to relocate "has been very much prompted" by Prince William and Kate Middleton's move to Adelaide Cottage from Kensington Palace. The Duchess of Sussex allegedly wants to ensure "that every time there's a story about Kate, she's not far behind."

However, one should take claims of a rivalry between Kate Middleton and Meghan Markle with a grain of salt. There is no proof that the latter is trying to upstage her sister-in-law and she has also not publicly spoken ill of her in any interviews.

Kate Middleton, Meghan Markle
From left: Kate Middleton at the Royal Variety Performance in London, 2014, Meghan Markle attending a presentation of A More Perfect Union: Stories of Prejudice and Power in West Hollywood 2012 Getty