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A modified Chaplygin gas model of unifying dark energy and dark matter with the exotic equation of state p = Bρ- A/ρα , which can also explain the recent expansion of the universe, is investigated by means of constraining the location of the peak of the cosmic microwave background radiation spectrum. We find that the result of CMBR measurements does not exclude the nonzero value of parameter B, but allows it in the range -0.35 (<~) B (<~) 0.025.