The time dependence of the transverse component of muon polarization in $K_{\mu 3}^{}{}_{}{}^0$ decay is calculated under the assumption that the $\Delta S=\Delta Q$ rule is violated. The initial beam is taken to be an arbitrary superposition of $K_L^{}{}_{}{}^0$ and $K_S^{}{}_{}{}^0$ states. Four form factors, $f_{\pm }$ for the $\Delta S=\Delta Q$ amplitude and $g_{\pm }$ for the $\Delta S=-\Delta Q$ amplitude, enter into the description of the decay. It is shown that when $f_{\pm }$ and $g_{\pm }$ are not proportional, the transverse polarization is significantly different from zero for the first few lifetimes of $K_S^{}{}_{}{}^0$ even when there is no $T$ violation in the decay. The possibility of experimentally observing this transverse polarization with muon decays from a regenerated $K_L^{}{}_{}{}^0$ beam is examined. It is found that the present experimental limits on $f_{\pm }$ and $g_{\pm }$ allow a transverse polarization as large as 15% at the exit face of the regenerator. This transverse polarization can, therefore, be used to test the $\Delta S=\Delta Q$ rule in $K_{\mu 3}^{}{}_{}{}^0$ decay.

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