The present invention concerns a method and an apparatus for producing a draftable staple fibre sliver (12) from a strand (12) of endless filaments, which is united and condensed for further processing. According to the invention the zone of the united and condensed sliver, from which, due to the cutting process, fibre points stick away inclined and pointed towards the front and outside, is inserted into the inside of the sliver.In this manner the detrimental effects, caused by the fibre points sticking out, are eliminated. Particularly the defective points in the end product produced, caused by these fibre points, are eliminated, fly waste generation in the processing room is reduced and, owing to the reduction of the danger of clogging of the fibre sliver guiding funnels, the operational reliability of the subsequent processing machines is improved.