It was a phrase coined by Sir Winston Churchill and has been used by successive British prime ministers over the intervening decades to describe the UK's strong bond with America.
But after a suggestion that Liz Truss is not overly keen on the term, the White House has offered to suspend use of the "special relationship".
In his first meeting with the Prime Minister on Wednesday, Joe Biden, the US president, instead told Ms Truss: "You’re our closest ally in the world."
But the term "special relationship" was conspicuously absent from Ms Truss' sit down with Mr Biden ahead of the pair's meeting at the United Nations in New York on Wednesday.
The White House later denied that the term had been "retired".
A senior official at first appeared surprised to hear reporters suggest that Ms Truss finds the phrase "a little bit demeaning".
"Demeaning of who?" replied the official, adding: "I mean, Joe Biden didn’t invent the phrase."
The official later quipped: “We'll shut it down until we can figure out what's going on.”
"I’m just kidding," the official added.
The idea of abandoning the term "special relationship" was first mooted by Boris Johnson, who was reported to believe it made the UK appear "needy and weak".
Downing Street later confirmed that the then-prime minister "prefers not to use the phrase", while stressing it "in no way detracts" from the importance of Britain's relationship with its closest ally.
There was speculation Mr Johnson's successor also dislikes the phrasing, which was adopted by Mr Churchill in one of his most significant post-war speeches in 1946.
But on Thursday night, Downing Street sources said Ms Truss was relaxed about the use of the phrase, and had even used it during her leadership bid.
In a speech as foreign secretary last year, Ms Truss stressed that Britain’s relationship with the US is “special but not exclusive”, stressing that "there are other allies too".
Ms Truss was also reported to have questioned the validity of the term during one of her first meetings as foreign secretary with Antony Blinken, her US counterpart.
The White House said Mr Biden had a "candid" discussion about the Northern Ireland Protocol, with the US president insisting it be kept and is a matter of "personal importance".
But officials said later that Mr Biden did not use a possible trade deal to threaten Ms Truss over Northern Ireland.