  We present an updated analysis of the rare decay
$K_{L}\to\pi^{0}\mu^{+}\mu^{-}$ within the Standard Model. In particular, we
present the first complete calculation of the two-photon CP-conserving
amplitude within Chiral Perturbation Theory, at the lowest non-trivial order.
Our results confirm previous findings that the CP-conserving contribution to
the decay rate cannot be neglected. By means of an explicit two-loop
calculation, we show that this contribution can be estimated with sufficient
accuracy compared to the CP-violating terms. We predict
$\cB(K_L\to\pi^0\mu^+\mu^-)_{\rm SM}=(1.5\pm0.3)\times10^{-11}$, with
approximately equal contributions from the CP-conserving component, the
indirect-CP-violating term, and the interesting direct-CP-violating amplitude.
The error of this prediction is mainly of parametric nature and could be
substantially reduced with better data on the $K_{S}\to\pi^{0}\ell^{+}\ell^{-}$
modes. The Standard Model predictions for various differential distributions
and the sensitivity to possible new-physics effects are also briefly discussed.
