Fastening device for fastening an assembly comprising at least two planar elements, the planar elements being provided with openings that face each other when the planar elements are in the assembly position, the fastening device comprising: a. a clip which is intended to be inserted into the openings of the planar elements and intended to hold the planar elements together between a first support point and a second support point, the clip comprising: i. a planar head for forming the first support point on the main surface of one of the planar elements, the planar head having a central opening in order to access an inner cavity of the clip; ii. two lateral upright members designed to form the second support point on another of the planar elements, the lateral upright members having a first end which is secured to the head as well as a second end, the second ends being connected to each other in such a way that the two lateral upright members define the inner cavity of the clip; b. a pin which is intended to be inserted into the inner cavity of the clip in order to lock the assembly; the fastening device being characterized in that the pin comprises at least one flexible bridging piece having a central portion which is connected to a main body of the pin by two flexible portions, the flexible bridging piece being intended to come into contact with a lateral upright member of the clip in order to force the second support point and to hold the assembled planar elements together. a. a clip which is intended to be inserted into the openings of the planar elements and intended to hold the planar elements together between a first support point and a second support point, the clip comprising: i. a planar head for forming the first support point on the main surface of one of the planar elements, the planar head having a central opening in order to access an inner cavity of the clip; ii. two lateral upright members designed to form the second support point on another of the planar elements, the lateral upright members having a first end which is secured to the head as well as a second end, the second ends being connected to each other in such a way that the two lateral upright members define the inner cavity of the clip; i. a planar head for forming the first support point on the main surface of one of the planar elements, the planar head having a central opening in order to access an inner cavity of the clip; ii. two lateral upright members designed to form the second support point on another of the planar elements, the lateral upright members having a first end which is secured to the head as well as a second end, the second ends being connected to each other in such a way that the two lateral upright members define the inner cavity of the clip; b. a pin which is intended to be inserted into the inner cavity of the clip in order to lock the assembly; the fastening device being characterized in that the pin comprises at least one flexible bridging piece having a central portion which is connected to a main body of the pin by two flexible portions, the flexible bridging piece being intended to come into contact with a lateral upright member of the clip in order to force the second support point and to hold the assembled planar elements together.