Pattern discovery in biological sequences (e.g., DNA sequences) is one of the most challenging tasks in computational biology and bioinformatics. So far, in most approaches, the number of occurrences is a major measure of determining whether a pattern is interesting or not. In computational biology, however, a pattern that is not frequent may still be considered very informative if its actual support frequency exceeds the prior expectation by a large margin. In this paper, we propose a new interesting measure that can provide meaningful biological information. We also propose an efficient index-based method for mining such interesting patterns. Experimental results show that our approach can find interesting patterns within an acceptable computation time.