Mutual information, as an association measure, has been used for various purposes as well as for calculating term similarity. There are, however, some limits in mutual information. It tends to emphasize low frequency terms extremely because the marginal value of mutual information changes inversely to frequency of terms. To compensate for this limit, this study suggests relative mutual information(RMI) coefficients which normalize mutual information, and examines their characteristics in some details. The RMI coefficients also improve effectiveness of global query expansion when they are adapted to three different collections.