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We developed a dynamic programming approach of computing common sequence structure patterns among two RNAs given their primary sequences and their secondary structures. Common patterns between two RNAs are defined to share the same local sequential and structural properties. The locality is based on the connections of nucleotides given by their phosphodiester and hydrogen bonds. The idea of interpreting secondary structures as chains of structure elements leads us to develop an efficient dynamic programming approach in time O(nm) and space O(nm), where n and m are the lengths of the RNAs. The biological motivation is given by detecting common, local regions of RNAs, although they do not necessarily share global sequential and structural properties. This might happen if RNAs fold into different structures but share a lot of local, stable regions. Here, we illustrate our algorithm on Hepatitis C virus internal ribosome entry sites. Our method is useful for detecting and describing local motifs as well. An implementation in C++ is available and can be obtained by contacting one of the authors.