The invention concerns a heart valve prosthesis. This prosthesis comprises a ring member for attachment to body tissue surrounding said ring; and a constriction system having anchoring pins for penetrating into the body tissue. The anchoring pins are arranged around the circumference of the ring member and adapted to move, when the pins have fully penetrated into the body tissue, the pins from a first penetrated position in a radial inward direction to a second penetrated position to constrict the body tissue.