An exchange option allows its holder to exchange one asset for another at maturity. In this short paper, the martingale approach, which is based on Continuous martingale representation theorem and Girsanov's theorem, is used to derive an explicit formula for the valuation of an exchange option with counterparty default. The volatilities of financial market considered here are all non-constant functions, which generalizes the results in [1] (Ammann, 2001).