Experiments on a sufficiently disordered two-dimensional (2D) electron system in silicon reveal a new and unexpected kind of metallic behavior, where the conductivity decreases as sigma (n_s,T)=sigma (n_s,T=0)+A(n_s)T^2 (n_s-carrier density) to a non-zero value as temperature T->0. In 2D, the existence of a metal with dsigma/dT>0 is very surprising. In addition, a novel type of a metal-insulator transition obtains, which is unlike any known quantum phase transition in 2D.
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