A fastener for fixing a mat to a carpet includes a female element having a cap and a female eyelet to sandwich a mat therebetween. A base element is engageable with the female element and includes a carpet holding arrangement for holding a carpet. The base element includes an enlarged head provided with an annular groove. The female eyelet includes at least two studs projecting inward, and deformable arms each of which extends between two adjacent studs transversely to a direction of pushing the head of the base element into the female eyelet. Each arm has a central portion disposed in the annular groove when the female element is engaged with the base element.