An osseous anchoring implant with cortical stabilization able to be implanted in an anchoring tissue, comprising: An expandable sleeve extending between a proximal portion having a first internal diameter, and a distal portion having a second internal diameter smaller than said first internal diameter, these two portions defining a longitudinal axis and said first and second internal diameters defining an internal profile of said expandable sleeve, and comprising, on the one hand, at least a first threading inside the expandable sleeve and, on the other hand, at least a second threading outside the expandable sleeve, A screw body extending between a proximal portion and a distal portion and having, on the one hand, along said longitudinal axis, an external profile complementary to the internal profile of said expandable sleeve and, on the other hand, at least one external threading whose screw pitch is reversed relative to said second external threading of the expandable sleeve, The implant being able to switch from a folded rest position to a deployed position by the actuation of said reversed threadings by causing the penetration of the screw into the expandable sleeve and generating the expansion of said expandable sleeve by deformation, thanks to the fact that the external diameter of the screw is greater, at least on a distal portion, than said second internal diameter of the expandable sleeve, by at least one shrinkage, In the deployed position of the implant, the second internal diameter of the expandable sleeve being greater than or equal to the first proximal diameter of the sleeve, wherein The sleeve has a cylindrical shape or a frustoconical portion obtained by said expansion, The implant has, in the vicinity of its proximal portion in the deployed position, a proximal frustoconical portion flaring towards the proximal portion and formed: Either by the external profile of said sleeve, or by the external profile of said screw body, or by the shape complementarity of the external profiles of the sleeve and of the screw body, in the deployed position, Said proximal frustoconical portion having an outer osseous anchoring threading (15, 252) over its periphery. An expandable sleeve extending between a proximal portion having a first internal diameter, and a distal portion having a second internal diameter smaller than said first internal diameter, these two portions defining a longitudinal axis and said first and second internal diameters defining an internal profile of said expandable sleeve, and comprising, on the one hand, at least a first threading inside the expandable sleeve and, on the other hand, at least a second threading outside the expandable sleeve, A screw body extending between a proximal portion and a distal portion and having, on the one hand, along said longitudinal axis, an external profile complementary to the internal profile of said expandable sleeve and, on the other hand, at least one external threading whose screw pitch is reversed relative to said second external threading of the expandable sleeve, The implant being able to switch from a folded rest position to a deployed position by the actuation of said reversed threadings by causing the penetration of the screw into the expandable sleeve and generating the expansion of said expandable sleeve by deformation, thanks to the fact that the external diameter of the screw is greater, at least on a distal portion, than said second internal diameter of the expandable sleeve, by at least one shrinkage, In the deployed position of the implant, the second internal diameter of the expandable sleeve being greater than or equal to the first proximal diameter of the sleeve, wherein The sleeve has a cylindrical shape or a frustoconical portion obtained by said expansion, The implant has, in the vicinity of its proximal portion in the deployed position, a proximal frustoconical portion flaring towards the proximal portion and formed: Either by the external profile of said sleeve, or by the external profile of said screw body, or by the shape complementarity of the external profiles of the sleeve and of the screw body, in the deployed position, Said proximal frustoconical portion having an outer osseous anchoring threading (15, 252) over its periphery. Either by the external profile of said sleeve, or by the external profile of said screw body, or by the shape complementarity of the external profiles of the sleeve and of the screw body, in the deployed position, Said proximal frustoconical portion having an outer osseous anchoring threading (15, 252) over its periphery.