A replacement valve for implantation centrally within the orifice of a malfunctioning native heart valve. The valve is designed for minimally invasive entry through an intercostal opening in the chest of a patient and an opening in the apex of the human heart. The replacement valve includes either a separate anchor (11, 87, 111) or a combined anchor (67) that folds around the malfunctioning native valve leaflets, sandwiching them in a manner so as to securely anchor the replacement valve in a precise, desired location.