Doubly-charged Higgs bosons are searched for in e(+)e(-) collision data collected with the L3 detector at LEP at centre-of-mass energies up to 209 GeV Final states with four leptons are analysed to tag the pair-production of doubly-charged Higgs bosons. No significant excess is found and lower limits at 95% confidence level on the doubly-charged Higgs boson mass are derived. They vary from 95.5 to 100.2 GeV, depending on the decay mode. Doubly-charged Higgs bosons which couple to electrons would modify the cross section and forward-backward asymmetry of the e(+)e(-) --> e(+)e(-) process. The measurements of these quantities do not deviate from the Standard Model expectations and doubly-charged Higgs bosons with masses up to the order of a TeV are excluded.