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Multimedia databases usually deal with huge amounts of data and it is necessary to have an indexing structure such that efficient retrieval of data can be provided. R-Tree with its variations, is a commonly cited indexing method. In this paper we propose an improved nearest neighbor search algorithm on the R-tree and its variants. The improvement lies in the removal of two hueristics that have been used in previous R*-tree work, which we prove cannot improve on the pruning power during a search.