Functional innovations after gene duplication may result in altered functional constraints between member gene clusters of a gene family. This type (type I) of functional divergence is measured by the coefficient of functional divergence (theta lambda), which can be interpreted as the decrease in rate correlation between gene clusters, or the probability that the evolutionary rate at a site is statistically independent between two gene clusters. A simple stochastic model has been developed for estimating theta lambda and testing its statistical significance. The current model includes the model of rate variation among sites as a special case when theta lambda = 0. Moreover, we have developed a site-specific profile based on the hidden Markov model to identify critical amino acid residues that are responsible for these functional differences between two gene clusters, which may have great potential in functional genomics.