An updated search for lepton flavor violating decays $\tau\to lll$ at BaBar

Recent results are presented on the search for non-conservation of lepton flavor in the decay of the tau lepton to three lighter leptons. The analysis is performed using $e^+e^- \to \tau^+\tau^-$ events collected between 1999 and 2006 at a center-of-mass energy near 10.58~GeV with the BaBar detector at the PEP-II storage rings at the Stanford Linear Accelerator Center.