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We show that the cross-phase modulation effect in a Sagnac fibre loop can be used to measure the nonlinear refractive index (n2) of the fibre. The setup is simpler than the counterparts that use the self-phase modulation effect but it gives greater sensitivity. The polarisation effect of the Sagnac loop can also be controlled and the reciprocal nature of the loop is ensured. This removes automatically the uncertainties from the thermal and some other sources.