Total prosthesis of a knee including a femoral element fitted with two condyles, a first of the condyles being external, a second of the condyles being internal, and a tibial plateau fitted with custom-made recesses to hold the condyles, wherein at least one of the condyles is integral on one of its sides with a convex cam ensuring posterior stability of the prosthesis. The tibial plateau has at least one track placed in the immediate vicinity of the recess holding the condyle integral with the cam, the at least one track being circumscribed by at least one curved abutment and at least one horizontal recess between posterior and anterior extremities of the tibial plateau. Provision is made between the condyles of the femoral element and the recesses of the tibial plateau for a free space and a notch for passage of a posterior cruciate ligament of a knee.