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We develop an approach to use nanostructured plasmonic materials as a nonmagnetic negative-refractive-index system at optical and near-infrared frequencies. In contrast to conventional negative-refraction materials, our design does not require periodicity and thus is highly tolerant to fabrication defects. Moreover, since the proposed materials are intrinsically nonmagnetic, their performance is not limited to the proximity of a resonance, so the resulting structure has relatively low loss. We develop the analytical description of the relevant electromagnetic phenomena and justify our analytic results via numerical solutions of Maxwell equations.