The temperature dependence of conductivity $sigma (T)$ in the metallic phase of a two-dimensional electron system in silicon has been studied for different concentrations of local magnetic moments. The local moments have been induced by disorder, and their number was varied using substrate bias. The data suggest that in the limit of $Tto 0$ the metallic behavior, as characterized by $dsigma/dT < 0$, is suppressed by an arbitrarily small amount of scattering by local magnetic moments.
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