MicroRNAs are a class of small non-protein coding RNAs that play an important role in the regulation of gene expression. Most studies on the identification of microRNA-mRNA pairs utilize the correlation coefficient as a measure of association. The use of correlation coefficient is appropriate if the expression data are available for several conditions and, for a given condition, both microRNA and mRNA expression profiles are obtained from the same set of individuals. However, there are many instances where one of the requirements is not satisfied. Therefore, there is a need for new measures of association to identify the microRNA-mRNA pairs of interest and we present two such measures. The first measure requires expression data for multiple conditions but, for a given condition, the microRNA and mRNA expression may be obtained from different individuals. The new measure, unlike the correlation coefficient, is suitable for analyzing large data sets which are obtained by combining several independent studies on microRNAs and mRNAs. Our second measure is able to handle expression data that correspond to just two conditions but, for a given condition, the microRNA and mRNA expression must be obtained from the same set of individuals. This measure, unlike the correlation coefficient, is appropriate for analyzing data sets with a small number of conditions. We apply our new measures of association to multiple myeloma data sets, which cannot be analyzed using the correlation coefficient, and identify several microRNA-mRNA pairs involved in apoptosis and cell proliferation.