The invention relates to an assembly comprising first and second parts made of composite material and held against each other by at least one fastener system comprising a rivet having a flat head from which there extends a shank having an enlarged end, and a washer co-operating with the enlarged end of the shank of the rivet, the head of the rivet bearing against a countersink formed in the first part, the washer bearing against the second part. On its face remote from its face bearing against the second part, the washer presents a portion of conical shape. The washer also has a central countersink with the enlarged end of the shank of the rivet pressing thereagainst.