Crosslapper, in particular arranged at the outlet from a carding device producing a web of fibers, in particular nonwoven fibers, comprising a front belt carrying the web of fibers in the crosslapper to an infeed or accumulator carriage, a rear belt carrying the accumulated web to a layering carriage and an apron on an upper strand (2; 2; 2) of which the layering carriage deposits the web accumulated by the accumulator carriage alternately on the bias in one direction and in the other direction to form a lap (N) moving at a speed V1(t) that varies as a function of time, in particular in a periodic manner, the crosslapper also comprising an output belt strand (20; 20; 20) on which the lap (N) leaves the crosslapper at a speed V2(t) that is different from the speed V1(t), in particular at a constant speed, the lap (N) undergoing at least one turn between the upper strand (2; 2; 2) and the output belt strand (20; 20; 20), in particular through 180, around a roller (3.2; 4.1; 3.7) mounted such that it can move in translation along the output belt strand (20; 20; 20), the lap (N) being sandwiched between another strand, turned in the opposite direction to the upper strand (2), of the apron and the output belt strand (20) and/or between another strand, turned in the opposite direction to the upper strand (2; 2), of the apron and an upper strand of an intermediate apron (30; 30) and/or between a lower strand of an intermediate apron (30; 30) and the output belt strand (20; 20).