The invention relates to the manufacture of composite sheets having a multiaxial fibrous reinforcement, which involves: forming a unidirectional lap of reinforcing threads, at least 50% by weight of which are co-blended threads consisting of reinforcing filaments and of filaments of an organic material which are intimately mixed, giving the said lap a cohesion allowing it to be lapped, lapping this lap on a support in movement, in a transverse direction in relation to the direction of movement, heating the reinforcing-thread/organic-material assembly, which is displaced in the direction of movement, and setting it by the action of heat, if appropriate by applying pressure, then cooling it to form a composite band, and collecting the said band in the form of one or more composite sheets. The present invention also relates to an apparatus for carrying out the method and to the products obtained.