  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 whose
measurements were made by Babar and Belle groups. We calculate the cross
section for this process in the Bethe-salpeter formalism under Covariant
Instantaneous Anstaz (CIA). To simplify our calculation, the heavy quark
approximation $(q<<M, P M)$ is employed in the quark and gluon propagators. In
the exclusive process of $e^{+}e^{-}$ annihilation into two heavy quarkonia,
the cross section calculated in this scenario is compatible with the
experimental data of Babar and Belle.
