A tubular prosthesis is radially deformable and includes a lattice that is deformable between a retracted state of small diameter and an expanded state of larger diameter. The prosthesis includes at least two outer hooks delimiting between them a clamp for engaging in an outer tissue. The two hooks are carried by the lattice and can be moved between a spaced-apart position in which the clamp is open and a closer-together position in which the clamp is closed. The prosthesis includes a guiding member for moving at least one of the hooks during deformation of the prosthesis. The guiding member delimits a guide passage in which at least one of the hooks is engaged.
