  Several claims have been made that we are located in a locally underdense
region of the Universe based on observations of supernovae and galaxy density
distributions. Two recent studies of K-band galaxy surveys have provided new
support for a local underdensity in the galaxy distribution out to distances of
200 - 300 Mpc. If confirmed, such large local underdensities would have
important implications on the interpretation of local measurements of
cosmological parameters. Galaxy clusters have been shown to be ideal probes to
trace the large-scale structure of the Universe. In this paper we study the
local density distribution in the southern sky with the X-ray detected galaxy
clusters from the REFLEX II cluster survey. From the normalized comoving number
density of clusters we find an average underdensity of ~30 - 40% in the
redshift range out to z ~0.04 (~170 Mpc) in the southern extragalactic sky with
a significance larger than 3.4sigma. On larger scales from 300 Mpc to over 1
Gpc the density distribution appears remarkably homogeneous. The local
underdensity seems to be dominated by the South Galactic Cap region. A
comparison of the cluster distribution with that of galaxies in the K-band from
a recent study shows that galaxies and clusters trace each other very closely
in density. In the South Galactic Cap region both surveys find a local
underdensity in the redshift range z= 0 to 0.05 and no significant underdensity
in the North Galactic Cap at southern latitudes. Our results to not support
cosmological models that attempt to interpret the cosmic acceleration by a
large local void, since the local underdensity we find is not isotropic and
limited to a size significantly smaller than 300 Mpc radius.
