An Improved Limit on Invisible Decays of Positronium

17 pages, 7 figures, added references, fixed limit on millicharged particles and changed two plots accordinglyThe results of a new search for positronium decays into invisible final states are reported. Convincing detection of this decay mode would be a strong evid ence for new physics beyond the Standard Model (SM): for example the existence of extra--dimensions, of milli-charged particles, of new light gauge bosons or of mirror particles. Mirror matter could be a relevant dark matter candidate. In this paper the setup and the results of a new experiment are presented. In a collected sample of about $(6.31\pm0.28) \times 10^6$ orthopositronium decay s, no evidence for invisible decays in an energy window [0,80] keV was found and an upper limit on the branching ratio of orthopositronium \invdecay could be set: $\binvdecay