In this paper we consider an analytical valuation of Basket Default Swaps. Our solution is based on a continuous-time model in a conditional independence framework. We use the order statistics of the default times of the names in the basket to find a recursive algorithm for computation of the risk-neutral distribution of the default process of the basket. We derive an analytical expression for the value of the first-to-default swap, which leads to a solution for an mth-to-default swap, using the recursive algorithm. The accuracy and performance of the analytical method are compared with that obtained using Monte Carlo simulation.