"This Charming Man" was the second single by The Smiths. The song was written by guitarist Johnny Marr and singer Morrissey. It did not appear on the UK release of the debut album. However, the US version of "The Smiths" had this song included.
The single peaked at number 25 on the UK Singles Chart.
Source (and more info): https://en.wikipedia.org/wiki/This_Charming_Man