A prosthetic valve assembly for implantation within a native aortic valve using a catheterization technique. The prosthetic valve assembly includes a collapsible and expandable metallic frame. The frame is constructed to resist the recoil forces of the native aortic valve. The frame may be formed with a concave profile. A valvular structure made with pericardial tissue is sewn to the frame for permitting blood flow in one direction. An internal cover is provided along an internal surface of the frame and provides a sleeve which prevents blood from passing through gaps in the frame.