A system that prevents stacked safe deposit box nests from shifting horizontally relative to one another utilizes registered pluralities of retainer brackets mounted along the upper and lower edges of the rear wall of the nest. The retainer brackets are configured with a central portion that is spaced away from the nest wall to define a vertically opening passageway. The retainer brackets along the lower edge of an overlying nest may then be aligned with the retainer brackets along the upper edge of an underlying nest by bringing the two nests into precise registration. A locking member is then passed through each aligned pair of retainer brackets.