New calculations of the Galactic contamination over microwave background radiation anisotropies are carried out. On the one hand, when a frequency-dependent contrast of molecular clouds with respect to the Galactic background of the diffuse interstellar medium is taken into account, the anisotropic amplitude produced by Galactic dust is increased with respect to previous calculations and this is of the same order as that of the data from the observations. On the other hand, if we take into account rotational dust emission, for instance, a frequency independence of anisotropies in the microwave range may be obtained. This leads to the possibility that under some particular, but not impossible, conditions all the microwave background radiation anisotropies may be due to Galactic foregrounds rather than cosmological in origin. Moreover, a suspected coincidence between the typical angular sizes of the microwave background radiation anisotropies and those of nearby molecular clouds makes more plausible the hypothesis of a purely Galactic origin for these anisotropies. It is also argued that the correlation among structures at different frequencies, the comparison of the power spectrum at different frequencies and the galactic latitude dependence of the anisotropies are not yet proofs in favour of either a cosmological or Galactic origin.