In this talk, we shall examine a variation of the Metropolis algorithm. This variation was proposed by Diaconis, Holmes, and Neal. It involves a duplication of the set of states which appears in the usual Metropolis algorithm. In the variation of the Metropolis algorithm, at each of the Markov chain the random process tries to go to a neighboring state determined by which duplicate the process is on at the start of the step. Like the usual Metropolis algorithm, the probability of actually going to the neighbor involves a ratio of the stationary probabilities of the 2 states. In this variation, an additional parameter controls the probability of going between the 2 duplicates of the set of states. Under certain conditions, this random process gets close to its stationary distribution faster than the corresponding ordinary Metropolis algorithm.