A prosthetic heart valve includes three bioprosthetic leaflets, each having an arcuate outer edge opposite a coapting edge and two tabs located on opposite sides of the coapting edge. The prosthetic heart valve also includes a self-expandable support frame defining three commissures spaced 120 degrees apart. Each commissure preferably includes two axially-extending attachment flanges with an axial slot therebetween. Each attachment flange includes a plurality of assembly holes through which sutures are passed to secure the leaflet tabs to the attachment flanges. The prosthetic heart valve also includes three outwardly flared U-shaped stabilizing members integrally formed with the leaflet support frame. The three stabilizing members having outer apices spaced 120 degrees apart and offset by 60 degrees from the three commissures. The stabilizing members are shaped to contact the surrounding aorta for stabilizing and anchoring the prosthetic heart valve in the implant position.