The anomalous properties of electromagnetic radiation from an antenna in the form of a rectangular section waveguide tube made of a metamaterial with the negative real parts of permittivity and permeability have been demonstrated. The metamaterial is an isotropic two-dimensional array of left and right-twisted coils placed on a thin polyurethane substrate. The coils of the sample are directed in equal numbers along the x, y, and z axes. The possibility of the preferential backward radiation of the structure has been shown on the basis of numerical calculations with the use of the method of moments and the measurements of the radiation pattern of the antenna in an anechoic chamber at frequencies close to the 3-GHz resonance frequency of the metamaterial. The causes and existence conditions of the effect have been revealed.