The music video for "Goodbye" was filmed at Mentmore Towers in Mentmore, Buckinghamshire on 1 and 2 November 1998, being directed by Howard Greenhalgh. It opens with each of the girls in four different black cars: 1957 Cadillac Fleetwood 75, 1941 Cadillac Fleetwood 75, 1955 Imperial Newport, 1958 Imperial Crown, and white wolves running. Girls arrive at a castle and walk up the stairs arm-in-arm. When they enter within dry ice clouds, there are frozen couples that the girls observe.
—Peter-Patrick76 (peter-patrick@mail.com)