An assembly comprising first and second parts made of composite material held one against the other by at least one fastener system comprising a bolt having a flat head from which there extends a threaded portion, and a nut having a flat head from which there extends a shank including tapping suitable for co-operating with the threaded portion of the bolt. The head of the bolt bears against a countersink formed in the first part. The head of the nut bears against a countersink formed in the second part. The fastener system is suitable, during axial expansion of the fastener system, for causing each head to tilt towards the countersink in which it is housed.