Study of double charmonium production in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>annihilation at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>≈</mml:mo><mml:mn>10.6</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi mathvariant="normal">G</mml:mi><mml:mi mathvariant="normal">e</mml:mi><mml:mi mathvariant="normal">V</mml:mi></mml:math>

We present a new analysis of double charmonium production in ${e}^{+}{e}^{\ensuremath{-}}$ annihilation. The observation of the processes ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}{\ensuremath{\eta}}_{c}$, $J/\ensuremath{\psi}{\ensuremath{\chi}}_{c0}$, and $J/\ensuremath{\psi}{\ensuremath{\eta}}_{c}(2S)$ is confirmed using a data set more than 3 times larger than that of Belle's previous report, and no evidence for the process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}J/\ensuremath{\psi}$ is found. We perform an angular analysis for $J/\ensuremath{\psi}{\ensuremath{\eta}}_{c}$ production and set an upper limit on the production of $J/\ensuremath{\psi}J/\ensuremath{\psi}$. Processes of the type ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\psi}(2S)(c\overline{c}{)}_{\mathrm{r}\mathrm{e}\mathrm{s}}$ have been observed for the first time; their rates are found to be comparable to those of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}(c\overline{c}{)}_{\mathrm{r}\mathrm{e}\mathrm{s}}$ processes.