The paper presents the theoretical study results of the dispersion characteristics of electromagnetic waves existing in antiferromagnetic (AFM) metamaterial. The AFM metamaterial consists of a transversely magnetized antiferromagnet, inside of which a two-dimensional periodic structure of thin conducting wires surrounded by insulators is placed. It has been established that the AFM metamaterial has two frequency ranges, in which there are backward waves, and the material pa-rameters of the medium are twice negative. The indicated areas are located in the terahertz range. Keywords: metamaterials, left-handed medium, antiferromagnetics, spin waves.