Abstract: A membrane applied to the ostium of an atrial appendage for blocking blood from entering the atrial appendage which can form blood clots therein is disclosed. The membrane also prevents blood clots in the atrial appendage from escaping therefrom and entering the blood stream which can result in a blocked blood vessel, leading to strokes and heart attacks. The membranes are percutaneously installed in patients experiencing atrial fibrillations and other heart conditions where thrombosis may form in the atrial appendages. A variety of means for securing the membranes in place are disclosed. The membranes may be held in place over the ostium of the atrial appendage or fill the inside of the atrial appendage. The means for holding the membranes in place over the ostium of the atrial appendages include prongs, stents, anchors with tethers or springs, disks with tethers or springs, umbrellas, spiral springs filling the atrial appendages, and adhesives.