The present invention provides a system and a method for closing septal defects and the like. The system includes a closure device having a pair of occluding disks, each disk being formed of a membrane and an elastically deformable frame carried about the periphery of the membrane. The frame, which may be formed of a superelastic material, is capable of being collapsed for passage through a catheter and elastically returning to a predetermined shape for tautly holding the membrane. A central portion of the membrane of each disk is attached to a central portion of the other membrane to define a conjoint disk. The method of the invention involves collapsing the frames of the disks, inserting the closure device into a catheter, and positioning the distal end of the catheter adjacent a septal defect. The first disk is then urged out of the distal end of the catheter to permit its frame to elastically return to a predetermined shape, pulling the membrane taut on one side of the defect. The second disk is then similarly deployed on another side of the defect, automatically positioning the conjoint disk within the defect to occlude it.