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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.