The present invention relates to a total knee prosthesis. This prosthesis includes a femoral implant (2) including two condyles (8, 9) delimiting between them an intercondylar notch (10), a tibial implant (3) intended to rest on the end of the tibia, and an articular insert (4) interposed between the tibial implant and the femoral implant and the upper surface of which (41) includes two glenoid cavities (18, 19) with an external profile (181, 191) congruent with the external profile (81, 91) of the condyles (7, 8) of the femoral implant and connected together through an interglenoidal connecting surface (20). According to the invention, the intercondylar notch (10) and the interglenoidal connecting surface (20) have congruent contact surfaces (101, 201) which are inscribed in two mating hyperbolic paraboloids and the contact surface (181, 191) of the glenoid cavities (18, 19) have in a horizontal section an ovoid shape and its inclined point (P) is located posteriorly to the line of larger width (L) of the insert.
