The present invention concerns a new intermediate material to be associated with a thermosetting resin for making composite parts, consisting of a unidirectional layer of carbon fibers with a weight of 100 to 280 g/m2, associated on each of its faces, with a web of thermoplastic fibers having a thickness of 0.5 to 50 microns, preferably 3 to 35 microns, the intermediate material having a total thickness of 80 to 380 microns, preferably from 90 to 320 microns, and a process for manufacturing composite parts from such a material and the resulting composite parts.