A sterile connector for the end of a conduit employed in the passage of blood or of blood components which comprises a resilient, deformable gasket disposed about the terminal end of a conduit, a continuous, removable yieldable flexible strip material, a portion of which is removably adhered to said gasket and overlies the end of said conduit, said strip material having a free end, said strip material being in a generally U-shaped configuration, whereby a force applied to the free end thereof withdraws the entire strip material to expose the end of said conduit; a method of joining the ends of two conduits together in a sterile manner so that blood or its components can pass therethrough which comprises providing each end with a connector as described above, arranging them in face-to-face alignment so that the ends of the conduit are in registry, drawing the connectors together so that the gasket of each connector is deformed inwardly and so that the free ends of the strip material are substantially parallel and withdrawing the strip material from each of said connectors at the same time; a pair of conduits joined together by a pair of facing connectors as described above.