Search for the non-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>D</mml:mi><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>decay<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ψ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>3770</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mo>→</mml:mo><mml:msubsup><mml:mi>K</mml:mi><mml:mi>S</mml:mi><mml:mn>0</mml:mn></mml:msubsup><mml:msubsup><mml:mi>K</mml:mi><mml:mi>L</mml:mi><mml:mn>0</mml:mn></mml:msubsup></mml:math>

Using the current world's largest data sample of $\ensuremath{\psi}(3770)$ decays, we present results of a search for the non-$D\overline{D}$ decay $\ensuremath{\psi}(3770)\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{L}^{0}$. We find no signal, and obtain an upper limit of $\ensuremath{\sigma}({e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\psi}(3770)\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{L}^{0})&lt;0.07\text{ }\text{ }\mathrm{pb}$ at 90% confidence level (CL). Our result tests a theoretical prediction for the upper bound on $\mathcal{B}(\ensuremath{\psi}(3770)\ensuremath{\rightarrow}{K}_{S}^{0}{K}_{L}^{0})$ based on a charmonia-mixing model.