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Comparative analysis of homologous sequences has been used to predict RNA secondary structure. However, most of existing comparative approaches are vulnerable to alignment errors and thus are not quite suitable for practical application. Here we devise a new method for predicting RNA secondary structure using multiple unaligned sequences. Our method completes the prediction in four major steps: 1) to detect all possible stems in each sequence using the so-called position matrix which indicates paired or unpaired information for each position in the sequence; 2) to find conserved stems across all sequences by multiplying the position matrices; 3) to assess the conserved stems and select some of them as the constraint for RNA folding; 4) to perform final structure prediction using RNAalifold, which is a popular program for secondary structure prediction. We tested our method on data sets composed of RNA sequences with known secondary structures. Our method has average accuracy 73.21% for two-sequence tests, 74.18% for three-sequence tests, and 79.75% for four-sequence tests. The results show that our method can predict RNA secondary structure with a higher accuracy than RNAalifold.