In the method in unwinding, paper web (W) is discharged from a reel (R1) that is becoming empty and the paper web of a new full reel (R2) is spliced at the discharge speed to the paper web discharged from the reel that is becoming empty. The terminal end point (L) of the web of the reel (R1) that is becoming empty is stored as information indicating its position in the longitudinal direction of the web in a readable memory (M) corresponding to the reel. During the discharge the distance travelled by the web is determined and compared to the memory, and when there is a predetermined length of web to the terminal end point (L) remaining on the reel (R1) that is becoming empty, a splicing command is given, whereafter the leading end of the paper web of a new full reel (R2) is spliced to the paper web (W) being discharged.