A fastener system is configured to fasten together at least two parts, one of which includes at least one flange that is caused to bear against a surface of the other part by a plurality of pins each presenting a collar having a non-circular outline. The collar is received in a groove formed in a bearing surface of one of the parts, and is designed to prevent the pins from turning by abutment against a wall, wherein the outline of each collar includes two substantially opposite plane surfaces that serve as mutual abutments against two adjacent collars.