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We numerically and experimentally investigated the negative refractive index effect in a single subwavelength magnetic “meta-atom,” a flower-shaped metamaterial (MM) structure. In our effort to understand the electromagnetic properties of flower-shaped structure, the third resonance has been considered for a rather high frequency in the gigahertz range of electromagnetic wave. It is found that the negative refractive index is a result of the tail of electric gap and the magnetic resonance at the third-order resonance. The effect is switched OFF by adjusting the density of flowers. In addition, the negative refractive index behavior is accompanied by polarization insensitivity resulting from its geometry. Finally, the electromagnetic and the loss properties of the MM were clarified at the third-order gap.