Unlike delta-hedging or similar methods based on Greeks, global hedging is an approach optimizing some terminal criterion that depends on the difference between the value of a derivative security and that of its hedging portfolio at maturity or exercise. Global hedging methods in discrete time can be implemented using dynamic programming. They provide optimal strategies at all rebalancing dates for all possible states of the world, and can easily accommodate transaction fees and other frictions. However, considering transaction fees in the dynamic programming model requires the inclusion of an additional state variable, which translates into a significant increase of the computational burden. In this short note, we show how a decomposition technique based on the concept of post-decision state variables can be used to reduce the complexity of the computations to the level of a problem without transaction fees.