We report the spectroscopic analysis of six kinematical members of the Zeta Reticuli Moving Group, one of them for the first time. We confirm the existence of the Group by establishing a common abundance pattern for four kinematical members. High resolution spectra yielded abundances of Si, Ca, Fe, Ni and Ba, and others. Effective temperatures were derived from the excitation & ionization equilibria of Fe lines of four stars. For these, and the remaining two members, temperatures were derived from colors and the fitting of theoretical spectra to the Hα line, and ages and masses were estimated from theoretical HR diagrams. We suggest that the Group is physical being metal-poor and ~6 Gyr old.