A search for pair-produced charged Higgs bosons is performed with the L3 detector at LEP using data collected at centre-of-mass energies between 192 and 202 GeV, corresponding to an integrated luminosity of 233.2 pb−1. Decays into a charm and a strange quark or into a tau lepton and its neutrino are considered. The observed events are consistent with the expectations from Standard Model background processes. Including data taken at lower centre-of-mass energies, lower limits on the charged Higgs mass are derived at the 95% confidence level. They vary from 67.4 to 79.9 GeV as a function of the H±→τν branching ratio.