Members Bono and The Edge stated that they recently rediscovered a number of old songs while they were remastering the record for its 25th anniversary reissue, scheduled for release later this year.
Speaking to Radio 1, The Edge said: "I listened to some tracks that we're gonna release with the new Unforgettable Fire reissue, some new songs that we discovered that we'd recorded, back in that era - the '80s - that we're gonna put out. And they sound amazing."
Bono noted that one track, titled 'Disappearing Act', is "incredibly special", while The Edge went on to say that the band have just completed putting the finishing touches to it in the studio.
The guitarist said: "Well, it was originally called 'White City', and it was a track we started with Brian Eno and Daniel Lanois back in 1983 when we were recording The Unforgettable Fire. And we discovered it about six months ago, and we dug it out and did some work on it in France a few weeks ago, and it's now finished."
Bono added: "It's 25 years ago, the drums, the bass and the guitar. And now, the voices. It is a strange, weird thing. And it's going out with The Unforgettable Fire reissue, but no-one's heard it."