We present a new analysis of double charmonium production in e(+)e(-) annihilation. The observation of the processes e(+)e(-)-->J/psieta(c), J/psichi(c0), and J/psieta(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(-)-->J/psiJ/psi is found. We perform an angular analysis for J/psieta(c) production and set an upper limit on the production of J/psiJ/psi. Processes of the type e(+)e(-)-->psi(2S)(c (c) over bar)(res) have been observed for the first time; their rates are found to be comparable to those of e(+)e(-)-->J/psi(c (c) over bar)(res) processes.
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