A device for fixing a bony structure to a support member (4), comprising: a main body (2) with first and second members (1J, 2J), the second member (2J) being movable in rotation with respect to the first member (1J), around a first axis (A) a flexible member (20) passing between the members (1J) and forming a loop (20P) around a bony structure and a clamping mechanism moving the first and second members (1J, 2J) into a clamping position, a support member (4) and the flexible member (20) being secured between the members (1J, 2J) in the clamping position. The first axis (A) being movable in translation along a first direction (D), the second member (2J) is movable in translation along the first direction (D). The clamping mechanism cooperates with the first and second members (1J, 2J) to move the second member (2J) in translation in the first direction (D).
