  We report the first observation of $\mPJpsi \to \mPeta\mPKst\mAPKst$ decay in
a $\mPJpsi$ sample of 58 million events collected with the BESII detector. The
branching fraction is determined to be $(1.15 \pm 0.13 \pm 0.22)\times
10^{-3}$. The selected signal event sample is further used to search for the
$\mPY$ resonance through $\mPJpsi \to \mPeta \mPY, \mPY\to\mPKst\mAPKst$. No
evidence of a signal is seen. An upper limit of \mathrm{Br}(\mPJpsi \to \mPeta
\mPY)\cdot\mathrm{Br}(\mPY\to\mPKst\mAPKst) < 2.52\times 10^{-4} is set at the
90% confidence level.
