Recent biochemical studies have indicated a number of regions in both the 16S and 23S rRNA that are exposed on the ribosomal subunit surface. In order to predict potential interactions between these regions we applied novel phylogenetically-based statistical methods to detect correlated nucleotide changes occurring between the rRNA molecules. With these methods we discovered a number of highly significant correlated changes between different sets of nucleotides in the two ribosomal subunits. The predictions with the highest correlation values belong to regions of the rRNA subunits that are in close proximity according to recent crystal structures of the entire ribosome. We also applied a new statistical method of detecting base triple interactions within these same rRNA subunit regions. This base triple statistic predicted a number of new base triples not detected by pair-wise interaction statistics within the rRNA molecules. Our results suggest that these statistical methods may enhance the ability to detect novel structural elements both within and between RNA molecules.