<p>Two principal physical properties of La₂CuO₄ and YBa₂Cu₃O₆ are identified, which can promote the emergence of superconductivity in unconventional high-temperature superconductors. The first property is a specific type of chemical bonding stimulating fluctuations of the charge density. To reveal it, it is necessary to carry out calculations of the electronic band structure and find the parameters of critical points in the charge density distribution in the crystal. For calculation of the electronic band structure of YBa₂Cu₃O₆ the same approach was applied, which we earlier used for the study of the electronic band structure of La₂CuO₄ and high-temperature superconductors: computer program WIEN2k and exchange potential of Becke and Johnston modified by Tran and Blaha. Such approach allowed us to obtain the antiferromagnetic ground state for the compound YBa₂Cu₃O₆ with a band gap <i>E</i>_g = 1.5&#xa0;eV and a magnetic moment on copper atoms <i>M</i>_Cu = 0.71 <i>μ</i>_B. It turned out that YBa₂Cu₃O₆ compound has a type of chemical bonding similar to that which we found earlier in La₂CuO₄ and in high-temperature superconductors. Consideration of the symmetry properties of the crystal structures of the La₂CuO₄ and YBa₂Cu₃O₆ compounds revealed a second characteristic property of them – the existence of magnetic crystal classes that admit a linear magnetoelectric effect. This effect allows the simultaneous existence of local magnetic fields and electric polarization in the sample. Based on two identified characteristic physical properties of the La₂CuO₄ and YBa₂Cu₃O₆ compounds, a roadmap is proposed for a search of new parent substances for obtaining unconventional high-temperature superconductors.</p>