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The probability of accepting a candidate move in the hybrid Monte Carlo algorithm can be increased by considering a transition to be between windows of several states at the beginning and end of the trajectory, with a particular state within the selected window then being chosen according to the Boltzmann probabilities. The detailed balance condition used to justify the algorithm still holds with this procedure, provided the start state is randomly positioned within its window. The new procedure is shown empirically to significantly improve the acceptance rate for a test system of uncoupled oscillators. It also allows expectations to be estimated using data from all states in the windows, rather than just states that are accepted.