A search for pair-produced doubly charged Higgs bosons has been performed using data samples corresponding to integrated luminosities of about 614 pb-1 collected with the OPAL detector at LEP at centre-of-mass energies between 189 and 209 GeV. No evidence for doubly charged Higgs boson production is observed. A mass limit of 96.7 GeV at the 95% confidence level has been set for the doubly charged Higgs particle in left-right symmetric models.