A locking member for a device for fastening ring sectors to an aircraft turbine engine casing is disclosed. The member has first and second clamping branches, which are connected together by curving joining portions, via a connecting branch. The joining portion of center thickness E1 has an inside surface of mean radius Rm1, and the joining portion of center thickness E2 has an inside surface of mean radius Rm2. Thickness E1 is strictly smaller than thickness E2, and mean radius Rm1 is strictly smaller than mean radius Rm2.