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In this work we study the process $e^{+}+e^{-}\longrightarrow J/\Psi+\eta_{c}$ at energy $\sqrt{s}= 10.6 GeV$ observed recently at B-factories whosemeasurements were made by Babar and Belle groups. We calculate the crosssection for this process in the Bethe-salpeter formalism under CovariantInstantaneous Anstaz (CIA). To simplify our calculation, the heavy quarkapproximation $(q<<M, P M)$ is employed in the quark and gluon propagators. Inthe exclusive process of $e^{+}e^{-}$ annihilation into two heavy quarkonia,the cross section calculated in this scenario is compatible with theexperimental data of Babar and Belle.

Cross section for double charmonium production in electron-positron annihilation at energy $\sqrt{s}$= 10.6 GeV