  Observing ROSAT sources in 20 x 25 deg centered at the high latitude active
star ER Eri, we found evidences for a new young nearby association (~30Myr
at~60pc), the Horologium Association (HorA), formed by at least 10 probable and
6 possible members, some being Post-T Tauri stars. We examine several
requirements that characterize a young association and they, together, create a
strong evidence for the reality of the HorA. In fact, the Li line intensities
are between those of the oldest classical T Tauri stars and the ones of the
Local Association stars. The space velocities of the HorA relative to the Sun,
U= -9.5+/-1.0, V = -20.9 +/- 1.1, W = -2.1 +/- 1.9, are not far from those of
the Local Association. We suggest that some hotter and non-X-ray active stars,
with similar space velocities, could be massive members of the HorA, among
them, the nearby Be star Achernar. The maximum of the mass distribution
function of the HorA is around 0.8 solar masses. At its distance, the projected
size of the HorA, ~50 pc, would be larger than our surveyed area and many other
members could have been missed. We also observed 3 control regions, two at
northern and southern galactic latitudes and a third one in the known TW Hya
Association (TWA), and the properties and distribution of their young stars
strengthen the reality of the HorA. Contrary to the TWA, the only known
binaries in the HorA are 2 very wide systems. The HorA is much more isolated
from clouds and older than the TWA and could give some clues about the lifetime
of the disks around T Tauri stars. Actually, none of the proposed members is an
IRAS source indicating an advanced stage of the evolution of their accreting
disks. ER Eri itself was found to be a RS CVn-like system.
