Abstract: First and second slivers (6, 5) are pieced together by the following steps: overlapping a trailing portion (6a) of a first sliver and a leading portion (5a) of a second sliver; introducing the overlapped portion (5a, 6a) into a drafting zone provided between a pair of lower and upper back rollers (11, 12) and a pair of lower and upper front rollers (13, 14) arranged along a sliver path from upstream to downstream; maintaining the peripheral speeds of the back and front rollers (11, 12; 13, 14) at the same speed, so that no draft is imparted to the overlapped portion until a leading end of the overlapped portion has reached the nip zone of the front rollers (13, 14); increasing only the peripheral speed of the front rollers (13, 14) to impart a predetermined draft to the overlapped portion until a trailing end thereof has passed through a nip zone of the back rollers (11, 12), whereby a thickness of the overlapped portion becomes substantially equal to the original proper sliver thickness; laterally rubbing th