  The pseudoscalar quarkonia exclusive decays to light mesons still poses a
challenge to the theoretical understanding of quarkonium properties in decay.
In this work, we evaluate the processes of pseudoscalar heavy quarkonium decays
into vector meson pairs, especially the helicity suppressed processes of
$\eta_b\rightarrow J/\psi J/\psi$ and $\eta_c\rightarrow VV$. In the frame of
NRQCD, the branching fraction of $Br[\eta_b\rightarrow J/\psi J/\psi]$ are
evaluated at the next-to-leading order of perturbative QCD; and within the
light-cone distribution formalism, we calculate also the higher twist effects
in these processes. Numerical results show that the higher twist terms
contribute more than what from the NLO QCD corrections in the process of
$\eta_b\rightarrow J/\psi J/\psi$. It is found that the experimental results on
$\eta_c\rightarrow VV$ are hard to be understood by merely the quark model and
perturbative QCD calculation.
