A textile machine is provided with apparatus for preparing the trailing end of a lap and a leading end of a fresh lap so that each end has a reduced fiber mass per unit length of lap in the prepared end. These lap ends are thereafter superimposed and joined together for subsequent processing in a combing unit of a combing machine or a drafting unit of a ribbon lap machine. The respective ends of the two laps may be prepared by a tearing action caused by clamping of the respective lap end between two spaced apart nip lines which are moved away from each other and wherein the spacing is slightly more than the length of the longest fiber in the lap. Preparation of a lap end may also be accomplished using a suction head for clamping of a lap along a nip line in order to carry out tearing of the lap to produced a prepared end.