Norman wrote the music for the first James Bond movie Dr. No and the signature theme of the James Bond franchise. Norman has received royalties since 1962 for the theme, but it was arranged by John Barry after the producers were dissatisfied with Norman's arrangement. Barry claimed that he actually did write the theme; nevertheless, Norman won two libel actions against publishers for claiming that Barry was the composer, most recently against The Sunday Times in 2001.
In the made-for-DVD documentary Inside Dr. No, Norman performs a piece of music he wrote for the stage several years earlier entitled Bad Sign, Good Sign, that resembles the melody of the "James Bond Theme" in several places.
Norman admits to having collected around £485,000 in royalties between the years 1976 and 1999 for the use of the theme since Dr. No.