A system for implanting a repair device onto a native valve of a natural heart to repair 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. The paddles and the gripping members are configured to attach to the native valve of the patient. The paddles are biased to the closed position, latched to the gripping members in the closed position, maintained in the closed position by a threaded connection, or otherwise maintained in the closed position.