A prosthesis for repairing a blood vessel, wherein the prosthesis is inserted intraluminally and fixed in the vessel so as to isolate a diseased section thereof and maintain the flow of blood from the vessel to collateral vessels involved the diseased section, and the prosthesis comprises a stent support and a flexible fabric liner of woven material comprising a plurality of concentric layers, wherein each of said layers has a very open fabric web which allows the passage of blood flow through the layers during the installation or the prosthesis but which allows the sealing of layers once the prosthesis is installed. A method is also provided for safe installation of the prosthesis.