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Efficient desalination of water continues to be a problem facing the society. Advances in nanotechnology have led to the development of a variety of nanoporous membranes for water purification. Here we show, by performing molecular dynamics simulations, that a nanopore in a single-layer molybdenum disulfide can effectively reject ions and allow transport of water at a high rate. More than 88% of ions are rejected by membranes having pore areas ranging from 20 to 60 Å(2). Water flux is found to be two to five orders of magnitude greater than that of other known nanoporous membranes. Pore chemistry is shown to play a significant role in modulating the water flux. Pores with only molybdenum atoms on their edges lead to higher fluxes, which are ∼ 70% greater than that of graphene nanopores. These observations are explained by permeation coefficients, energy barriers, water density and velocity distributions in the pores.