This paper proposes a self-financing trading strategy that minimizes the expected shortfall locally when hedging a European contingent claim. A positive shortfall occurs if the hedger is not willing to follow a perfect hedging or a superhedging strategy. In contrast to the classical variance criterion, the expected shortfall criterion depends only on undesirable outcomes where the terminal value of the written option exceeds the terminal value of the hedge portfolio. Searching a strategy which minimizes the expected shortfall is equivalent to the iterative solution of linear programs whose number increases exponentially with respect to the number of trading dates. Therefore, we partition this complex overall problem into several one-period problems and minimize the expected shortfall only locally, i.e. only over the next trading period. This approximation is quite accurate and the number of linear programs to be solved increases only linearly with respect to the number of trading dates.