Dental prosthesis fixing device comprising: • an interface piece adapted to be fixed to an implant by means of fixing means defined throughout at least a part of said interface piece, where said interface piece in turn comprises: ∘ a coupling which is found at an upper end of the interface piece and preferably defined by a revolution solid, ∘ a polygonal rib, defined by a flat base whereon the revolution solid is found, which will fundamentally allow the tightening of the interface piece to the implant already inserted in its corresponding place and already fixed to it, ∘ a preferably circular base located after the rib and just below it on the side opposite that where the revolution solid is found, • a connection piece associated to the prosthesis and designed to act as retention element on being fixed to the interface piece, wherein said connection piece comprises: ∘ a retainer, at an apical part of the connection piece, and comprising a hollow inner zone defined by an essentially larger revolution volume and coinciding with that of the revolution solid of the interface piece, and ∘ a case with a form in its inner zone of equal or greater size than that of the retainer, a case which is located so that it surrounds at least partially the retainer; the fixing device being characterized in that a apical edge of said case is in total contact with at least a perimeter zone of the area of the base. • an interface piece adapted to be fixed to an implant by means of fixing means defined throughout at least a part of said interface piece, where said interface piece in turn comprises: ∘ a coupling which is found at an upper end of the interface piece and preferably defined by a revolution solid, ∘ a polygonal rib, defined by a flat base whereon the revolution solid is found, which will fundamentally allow the tightening of the interface piece to the implant already inserted in its corresponding place and already fixed to it, ∘ a preferably circular base located after the rib and just below it on the side opposite that where the revolution solid is found, ∘ a coupling which is found at an upper end of the interface piece and preferably defined by a revolution solid, ∘ a polygonal rib, defined by a flat base whereon the revolution solid is found, which will fundamentally allow the tightening of the interface piece to the implant already inserted in its corresponding place and already fixed to it, ∘ a preferably circular base located after the rib and just below it on the side opposite that where the revolution solid is found, • a connection piece associated to the prosthesis and designed to act as retention element on being fixed to the interface piece, wherein said connection piece comprises: ∘ a retainer, at an apical part of the connection piece, and comprising a hollow inner zone defined by an essentially larger revolution volume and coinciding with that of the revolution solid of the interface piece, and ∘ a case with a form in its inner zone of equal or greater size than that of the retainer, a case which is located so that it surrounds at least partially the retainer; ∘ a retainer, at an apical part of the connection piece, and comprising a hollow inner zone defined by an essentially larger revolution volume and coinciding with that of the revolution solid of the interface piece, and ∘ a case with a form in its inner zone of equal or greater size than that of the retainer, a case which is located so that it surrounds at least partially the retainer;