  We search for a light Higgs boson $A^0$ in the fully reconstructed decay
chain of $J/\psi \rightarrow \gamma A^0$, $A^0 \rightarrow \mu^+\mu^-$ using
$(225.0\pm2.8)\times10^6$ $J/\psi$ events collected by the BESIII experiment.
The $A^0$ is a hypothetical CP-odd light Higgs boson predicted by many
extensions of the Standard Model including two spin-0 doublets plus an extra
singlet. We find no evidence for $A^0$ production and set $90\%$
confidence-level upper limits on the product branching fraction
$\mathcal{B}(J/\psi \rightarrow \gamma A^0) \times \mathcal{B}(A^0 \rightarrow
\mu^+\mu^-)$ in the range of $(2.8-495.3)\times 10^{-8}$ for $0.212 \le m_{A^0}
\le 3.0$ GeV/c$^2$. The new limits are $5$ times below our previous results,
and the nature of the $A^0$ is constrained to be mostly singlet.
