An arrangement (001; 101; 202; 302; 402) for fastening an element on a support surface (002; 102; 202; 302; 402), the arrangement comprising at least one rail (020; 120; 220; 320; 420) comprising a lower face (021; 121; 212; 312; 421), an upper face (022; 122; 222; 322; 422) and a protruding part (028, 128, 228) the lower face (021; 121; 212; 312; 421) coming into contact with the support surface (002; 102; 202; 302; 402); at least one substantially rectangular mounting part (030; 130; 230; 330; 430) comprising a base plate (031; 131; 231; 331; 431) which defines a lower face (032; 132; 232; 332; 432) and an upper face (039; 139; 239; 439), the upper face (039; 139; 239; 439) comprising anchoring means (040; 140; 240; 340; 440); at least one element to be fastened, the element having a lower face, which comprises at least one recess, the recess being arranged so as to engage with the anchoring means of the mounting part; wherein the rail (020; 120; 220; 320; 420) comprises a C-profile (024; 124; 224; 324; 424) which is open on the upper-face side (022; 122; 222; 322; 422) and defines a profile width (025; 125; 225; 325; 425) and a profile height (026; 126; 226; 326; 426), the C-profile (024; 124; 224; 324; 424) being adapted to receive the mounting part (030; 130; 230; 430), and wherein the rail comprises a toothed surface (027; 127; 227; 327) extending on its upper-face; wherein the base plate (031; 131; 231; 331; 431) of the mounting part (030; 130; 230; 330; 420) has a width (034; 134; 234; 334; 434) which corresponds substantially to the profile width (025; 125; 225; 325; 425) of the rail (020; 120; 220; 320; 420), and a thickness (033; 133; 233; 333; 433) which corresponds substantially to the profile height (026; 126; 226; 326; 426) of the rail, making it possible to slide the mounting part (030; 130; 230; 330; 430) along the profile (024; 124; 224; 324; 424) and to hold the mounting part (030; 130; 230; 330; 430) in the rail (020; 120; 220; 320; 420); wherein the base plate (031; 131; 231; 331; 431) comprises, on its lower face (032; 132; 132; 332, 432), a structure comprising at least one tooth (043; 143; 343; 434), said at least one tooth cooperating with said toothed surface when the mounting part is held by the rail; wherein the anchoring means of the mounting part comprises at least one foot which is substantially perpendicular to the base plate, the foot being equipped on one face with at least one tenon which projects at right angles to the foot, said tenon being dimensioned so as to cooperate with a counterpart profile groove in a wall of the recess of the element to be fastened; characterized in that the foot of the mounting part and the recess of the element to be fixed are dimensioned so that at least a part of the lower face of the element to be fixed rests on the upper surface of the rail, when said foot is engaged in said recess; wherein the anchoring means and the grooved recess are configured in such a way that the element to be fastened is attached to the mounting part by a first movement, said first movement engaging the foot in the recess without the tenon penetrating the groove, and in such a way that the element may then be displaced in a direction perpendicular to the first movement to engage the tenon in the groove; wherein the mounting part comprises at least one stop on the upper face of the base plate, the at least one stop being situated on the side opposite the side of the foot carrying the tenon.