A system for implanting a repair device onto a native valve of a natural heart to repairing the native valve of a patient during a non-open-heart procedure. The system includes a pair of paddles and a pair of gripping members. The paddles are movable between an open position and a closed position. Each of the gripping members has a barbed portion for securing the gripping members to the native valve of a patient. Each gripping member is slidably attached to a corresponding paddle. Each gripping member can be moved in a first direction along the paddle before the barbed portion of the gripping member pierces the native valve of the patient. Each gripping member can be moved in a direction substantially opposite the first direction after the barbed portion pierces the native valve of the patient such that the gripping members create a tensioning force on the native valve of the patient.