A reel unwinder including a first unwinding position, in which a first reel is positioned; a second unwinding position, to which the first reel is transferred when it is replaced with a second reel; a stand-by position, in which the second reel is kept in stand-by; a first unwinding member adapted to start rotation of the second reel when the first reel is replaced with the second reel. Moreover, the unwinder includes a second unwinding member, with at least one endless flexible element. The endless flexible element extends from the first unwinding position to the second unwinding position, and is adapted to maintain the first reel in contact with the second unwinding member and in rotation by the second unwinding member in the first unwinding position, in the second unwinding position and while it is being transferred from the first unwinding position to the second unwinding position.