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The existence of free–free absorption in the nucleus of Cen A was suggested by Tingay & Murphy in 2001 as an explanation for the large value of the spectral index between 2.2 and 5 GHz. In this paper we present further evidence for this absorption, based on the observations of short time-scale variability at mm wavelengths and their lack of correlation with X-ray emission, as expected if they were both originated in the same physical process. To explain the short-term variability, we assumed that the mm-wave emission is produced near the base of the inhomogeneous parsec-scale jet that has a bulk velocity of about 0.5 c. The presence of an ionized media between the jet and the observer will produce the observed 7-mm flux density variability, as different jet features move behind the absorbing material. We estimated that a region with 5 × 106 electrons cm−3 and 1.5 × 1015 cm radius can explain the intensity and the duration of the mm-flux variations, but the corresponding column density would not be enough to absorb significantly the X-ray flux, explaining the lack of correlation between the radio and X-ray variability. The upper limit for the cloud size inferred for the absorbing region shows that the media surrounding the core of Cen A must be clumpy. [ABSTRACT FROM AUTHOR]