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In this paper, amplified double Rayleigh backscattering noise (DRB) in the optical fibre Raman amplifier is analysed. Expressions are presented for both forward pumping and backward pumping schemes. Calculation is performed to show the effective suppression of DRB noise by employing an optical isolator. The optimal position for the isolator is determined and is found to be insensitive to the power levels of the signals and pumps. The results show that a reduction of the DRB noise by almost 2 to 3 orders can be reached.