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N. Metropolis's (1953) algorithm has often been used for simulating physical systems that pass among a set of states, with the probabilities of the system being in such states distributed like the Boltzmann function. There are literally thousands of different applications in the physical sciences and elsewhere. In this article, we explain how to reformulate the basic Metropolis algorithm so as to avoid the do-nothing steps and reduce the running time, while also keeping track of the simulated time as determined by the Metropolis algorithm. By the simulated time, we mean the number of Monte Carlo steps that would have been taken if the basic Metropolis algorithm had been used. This approach has already proved successful when used for parallel simulations of molecular beam epitaxy. We show an example.