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In this paper we present a heuristic algorithm, iterative loop matching, for predicting RNA pseudoknots. The method can utilize either thermodynamic or comparative information or both, thus is able to predict for both aligned and individual sequences. Using 8-12 homologous sequences, the algorithm correctly identifies more than 90% of base-pairs for short sequences and 80% overall. It correctly predicts nearly all pseudoknots, while having very few false predictions. Comparisons show that our algorithm is more sensitive and more specific than existing methods. In addition, our algorithm is very efficient and can be applied to sequences up to several thousands of bases long.