The group, who are currently on an American promotional tour, claim that the song sounds too unusual to be successful in the States.
"'Don't Upset The Rhythm' is not for mainstream radio out there so we're leaving it for the indie stations," drummer Jamie Morrison told The Daily Star.
"We also don't want to be going backwards doing promo," he added. "We've toured America probably more than anywhere else so feel quite established and have enough good songs on the album to release."
The song, which is taken from their second LP Wild Young Heart, reached number two in the UK when it was released in April.