A secure installing system for mounting a container on a frame member, with ease of access to the container. The installing system is appropriate for use in a medical environment such as a hospital. The frame member may be a shelf bracket, or a cabinet for housing a medical waste container, and may be mounted to a wall. A container such as a glove box holder is installed on the frame member. The container may have a dispenser opening providing ready access to materials such as tissues or surgical gloves. The container is securely mounted to the frame member using a hook and snap arrangement and may be disengaged from the frame member in order to exchange stored materials such as tissues or surgical gloves. The hook and snap arrangement protect against accidental dislodging of the container from the frame member, thereby preventing possible contamination of stored materials. Frame members that are shelf brackets may support two containers each. Furthermore, shelf brackets may be joined and latched together in alignment for storage of multiple containers.