Conditional independence reasoning has been shown to be helpful in the context of Bayesian nets to optimize probabilistic inference, and related techniques have been applied to speed up a number of logical reasoning tasks in boolean logic by eliminating irrelevant parts of the formulas. This paper shows that conditional independence reasoning can also be applied to optimize epistemic model checking, in which one verifies that a model for a number of agents operating with imperfect information satisfies a formula expressed in a modal multi-agent logic of knowledge. An optimization technique is developed that precedes the use of a model checking algorithm with an analysis that applies conditional independence reasoning to reduce the size of the model. The optimization has been implemented in the epistemic model checker MCK. The paper reports experimental results demonstrating that it can yield multiple orders of magnitude performance improvements.