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By analyzing a data sample of 2.93 fb$^{-1}$ collected at $\sqrt s=$ 3.773GeV with the BESIII detector operated at the BEPCII storage rings, we measurethe branching fractions ${\mathcal B}(D^0\to\omega\eta)=(2.15\pm0.17_{\rmstat.}\pm0.15_{\rm sys.})\times 10^{-3}$, ${\mathcalB}(D^0\to\eta\pi^0)=(0.58\pm0.05_{\rm stat.}\pm0.05_{\rm sys.})\times 10^{-3}$,${\mathcal B}(D^0\to\eta^\prime\pi^0)=(0.93\pm0.11_{\rm stat.}\pm0.09_{\rmsys.})\times 10^{-3}$, ${\mathcal B}(D^0\to\eta\eta)=(2.20\pm0.07_{\rmstat.}\pm0.06_{\rm sys.})\times 10^{-3}$ and ${\mathcalB}(D^0\to\eta^\prime\eta)=(0.94\pm0.25_{\rm stat.}\pm0.11_{\rm sys.})\times10^{-3}$. We note that ${\mathcal B}(D^0\to \omega\eta)$ is measured for thefirst time and that ${\mathcal B}(D^0\to \eta\eta)$ is measured with muchimproved precision.

Measurements of the Branching Fractions of the Singly-Cabibbo-Suppressed Decays $D^0\to\omega\eta$, $\eta^{(\prime)}\pi^0$ and $\eta^{(\prime)}\eta$