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The 1/f noise in multiwalled carbon nanotubes bundles has been investigated between the frequency range of 0.1 to 30 Hz. At room temperature the noise spectrum is standard 1/f and its level is proportional to the square of the bias voltage. With decreasing temperature the noise level also decreases. At 4.2 K the noise level follows a non-monotonic dependence against the bias voltage, showing a peak at a certain bias voltage, meanwhile its frequency dependence also deviates from the 1/f trend. This anomalous behaviour is discussed within the picture of environmental quantum fluctuation of charge transport in the samples.