The longitudinal polarization, the transverse polarization, and the forward-backward asymmetry of ΛΛ baryons, have been measured using a sample of 4.34 million hadronic Z0Z0 decays collected with the OPAL detector at LEP between 1990 and 1995. These results are important as an aid to the understanding of hadronization mechanisms. Significant longitudinal polarization has been observed at intermediate and high momentum. For xExE ( ≡2EΛ/s√)>≡2EΛ/s)> 0.3, the longitudinal polarization has been measured to be −32.9±5.5−32.9±5.5 (stat) ±± 5.2 (syst)%. We have observed no transverse polarization. A significant forward-backward asymmetry has been measured and can be described by a JETSET model.