A crosslapper receives a card web and folds it into a lap intended to be needle-punched or consolidated by other ways. The web includes zones which are more condensed, having a spectrum of orientation of fibers with a component parallel to the width of the web, alternating with less condensed zones having a longitudinal unidirectional spectrum of orientations. The zones which are less condensed are used to form the edge zones of the lap. The result is that the lap has different respective spectra of orientation which pre-compensate for the unwanted changes produced by the needle-punching or other consolidation which follows. A needle-punched lap is obtained having a uniform MD/CD ratio (relationship between longitudinal and respectively transverse tensile strengths) or having a sought profile of the MD/CD ratio across the width of the lap.