A positioning system is provided, comprising a support beam for attachment to an individual's jaw, and a removable denture comprising a bottom surface formed with a recess configured for receiving therein the support beam, the support beam and the recess being configured to preclude movement therebetween when the support beam is fully received within the recess. The support beam or the recess comprises one or more positioning grooves extending parallel to a path of insertion of the denture, and the other comprises one or more positioning protrusions laterally projecting therefrom and configured to be slidingly received within a corresponding positioning groove to provide at least a partially snug fit. The one or more positioning grooves and the corresponding one or more positioning protrusions are configured on one or more of a labial, lingual, or an face extending between the labial and lingual faces, of the recess and the support beam.