A fastening device for a false ceiling, the false ceiling comprising: - a plurality of inverted-T-shaped section bars (220,240; 320,340) having a direction of longitudinal extension each comprising: o a base (222; 322); o a vertical body (225; 325) comprising two facing vertical walls (225a; 325A) each with a first vertical wall end and a second vertical wall end opposite to said first vertical wall end, wherein the two facing vertical walls form an open space in the direction that moves away from the base, and the first vertical wall end is fixed to said base (222; 322); - a plurality of first inverted-T-shaped section bars (220; 320) in said plurality of inverted-T-shaped section bars, wherein in each first inverted-T-shaped section bar the two facing vertical walls (225a; 325a) are connected by or accommodate a cross-bar (225b, 253; 325b, 353) which includes a vertical hole (253a; 353a) which is configured to receive a clamping screw (251; 351) in screwing connection; and - a plurality of second inverted-T-shaped section bars (240; 340), said second inverted-T-shaped section bars (240; 340) being configured to be arranged transversely to said first inverted-T-shaped section bars (220; 320) so that a second inverted-T-shaped section bar is placed onto the base of the first inverted-T-shaped section bar in such a way that the first and second inverted-T-shaped section bars are at the same height; wherein:: - the fastening device comprises an elongated body (252; 352) with a through hole (257; 357) configured to receive the clamping screw (251; 351); - said elongated body (252; 352) being configured to push, in use, at least one of said plurality of second inverted-T-shaped section bars (240; 340) toward said base (222; 322) of the first inverted-T-shaped section bars; the fastening device being characterized in that said elongated body (252; 352) comprises: - transverse projections (254; 354), which are configured to penetrate, in use, into the open space of the second inverted-T-shaped section bar - two notches (255, 355) provided laterally to said transverse projections and configured to rest on the second inverted-T-shaped section bar (240, 340), the two notches being provided at the free end of the transverse projection; and - lateral protrusions (256; 356) which are placed in the middle between said opposite ends and extend transversely to said main direction, the lateral protrusions being configured to penetrate, in use, into the open space of the first inverted-T-shaped section bar so as to ensure the square angle positioning of the first inverted-T-shaped section bar (220; 320). - a plurality of inverted-T-shaped section bars (220,240; 320,340) having a direction of longitudinal extension each comprising: o a base (222; 322); o a vertical body (225; 325) comprising two facing vertical walls (225a; 325A) each with a first vertical wall end and a second vertical wall end opposite to said first vertical wall end, wherein the two facing vertical walls form an open space in the direction that moves away from the base, and the first vertical wall end is fixed to said base (222; 322); o a base (222; 322); o a vertical body (225; 325) comprising two facing vertical walls (225a; 325A) each with a first vertical wall end and a second vertical wall end opposite to said first vertical wall end, wherein the two facing vertical walls form an open space in the direction that moves away from the base, and the first vertical wall end is fixed to said base (222; 322); - a plurality of first inverted-T-shaped section bars (220; 320) in said plurality of inverted-T-shaped section bars, wherein in each first inverted-T-shaped section bar the two facing vertical walls (225a; 325a) are connected by or accommodate a cross-bar (225b, 253; 325b, 353) which includes a vertical hole (253a; 353a) which is configured to receive a clamping screw (251; 351) in screwing connection; and - a plurality of second inverted-T-shaped section bars (240; 340), said second inverted-T-shaped section bars (240; 340) being configured to be arranged transversely to said first inverted-T-shaped section bars (220; 320) so that a second inverted-T-shaped section bar is placed onto the base of the first inverted-T-shaped section bar in such a way that the first and second inverted-T-shaped section bars are at the same height; - the fastening device comprises an elongated body (252; 352) with a through hole (257; 357) configured to receive the clamping screw (251; 351); - said elongated body (252; 352) being configured to push, in use, at least one of said plurality of second inverted-T-shaped section bars (240; 340) toward said base (222; 322) of the first inverted-T-shaped section bars; - transverse projections (254; 354), which are configured to penetrate, in use, into the open space of the second inverted-T-shaped section bar - two notches (255, 355) provided laterally to said transverse projections and configured to rest on the second inverted-T-shaped section bar (240, 340), the two notches being provided at the free end of the transverse projection; and - lateral protrusions (256; 356) which are placed in the middle between said opposite ends and extend transversely to said main direction, the lateral protrusions being configured to penetrate, in use, into the open space of the first inverted-T-shaped section bar so as to ensure the square angle positioning of the first inverted-T-shaped section bar (220; 320).