A search for pair-produced doubly charged Higgs bosons has been performed using data samples corresponding to an integrated luminosity of about $614\,\rm pb^{-1}$ collected with the OPAL detector at LEP at centre-of-mass energies between 189~GeV and 209~GeV. No evidence for a signal has been observed. A mass limit of 98.5~GeV/$c^{2}$ at the 95\% confidence level has been set for the doubly charged Higgs particle in left-right symmetric models. This is the first search for doubly charged Higgs bosons at centre-of-mass energies larger than 91~GeV.