1. An apparatus for maintaining an aseptic chain of sterility during medical cleaning of a bacteriologically contaminated appliance in an ultrasonic cleaning machine, the apparatus comprising: a rigid cylindrical container having an open top, side walls, and a closed base end; a disposable, bacteriologically impermeable sheath formed of a flexible material, the sheath having an open end provided with elastic means for gripping an outer upper periphery of the top of the container when the sheath is inserted therein, a closed end connected to the open end by a substantially cylindrical side wall and having a rigid O-ring-shaped member formed peripherally around the closed end to facilitate insertion of the sheath into the container, with the open end of the sheath being detachably closely fitted by the elastic means over the outer upper periphery of the open top of the container, the closed end of the sheath being disposed adjacent to an inner surface of the closed base end of the container, the rigid O-ring-shaped member being disposed substantially in contact with a juncture between the closed base end inner surface of the container and an inner surface of the sidewalls of the container; and a sterilizing liquid filling the sheath, the liquid covering an appliance disposed within the sheath to be medically cleaned.