An undersea flexible pipe for conveying hydrocarbons, the pipe including from the inside to the outside an inner sealing sheath, at least one ply of traction armors wound about the inner sealing sheath, a deformable holding layer including at least one flexible ribbon or holding band wound about the traction armor ply, and at least one tubular structure surrounding the holding layer, wherein the ribbon includes fiber strands oriented substantially in the longitudinal direction of the ribbon. The ribbon is covered by a reinforcing layer of a polymer material for the deformation resistance of the holding layer.