A search for R-parity conserving charginos and neutralinos, predicted by supersymmetric theories, is performed using a data sample of about 435~pb$^{-1}$ taken at centre-of-mass energies of 192 to 209~GeV with the OPAL detector at LEP in the years 1999 and 2000. No evidence for chargino or neutralino production is found. Upper limits on chargino and neutralino pair production (${\tilde{\chi}^+}_1 {\tilde{\chi}^-}_1$, ${\tilde{\chi}^0}_1 {\tilde{\chi}^0}_2$) cross-sections are obtained as a function of the chargino mass ($m_{\tilde{\chi}^\pm}$), the lightest neutralino mass ($m_{{\tilde{\chi}^0}_1}$) and the second lightest neutralino mass ($m_{{\tilde{\chi}^0}_2}$)\@.