A percutaneously inserted bistable heart valve prosthesis is folded inside a catheter for transseptal delivery to the patient's heart for implantation. The heart valve has an annular ring, a body member having a plurality of legs, each leg connecting at one end to the annular ring, claws that are adjustable from a first position to a second position by application of external force so as to allow ingress of surrounding heart tissue into the claws in the second position, and leaflet membranes connected to the annular ring, the body member and/or the legs, the leaflet membranes having a first position for blocking blood flow therethrough and a second position for allowing blood flow therethrough. The heart valve is designed such that upon removal of the external force the claws elastically revert to the first position so as to grip the heart tissue positioned within the claws, thereby holding the heart valve in place. The body member and claws may be integrated into a one-piece design. The heart valve may be used as a prosthesis for the mitral valve, aortic valve, pulmonary valve, or tricuspid valve by adapting the annular ring to fit in a respective mitral, aortic, pulmonary, or tricuspid valve opening of the heart.