A clip for immobilizing leaflets of a cardiac or venous valve includes a hub having a pair of tangle resistant spring-biased outer arms coupled to an inferior end of the hub and a pair of tangle resistant spring-biased inner arms adjacent to the outer arms and coupled to a superior end of the hub. A delivery catheter may be used to position the valve clip adjacent a target valve while the outer and inner arms are biased in an opened position relative to each other. After the valve leaflets are located between the opened outer and inner arms, the biasing forces may be released to allow the clip to self-close the clip over the valve leaflets.