Recently, we succeeded in detwinning REBa2Cu3O7 (RE123, RE = rare-earth elements)-coated conductors by annealing under an external uniaxial strain. Using the untwinned RE123 tapes, the uniaxial-strain dependencies of the critical temperature Tc along the a and b crystal axes were investigated over a wide strain region from compression to tension. We found that the strain dependencies of Tc for the a and b axes obey a power law but exhibit opposite slopes. In particular, the maximum value of Tc is obtained when the CuO2 plane becomes a square, and its lattice constant is close to 0.385 nm. It is suggested that a tetragonal structure with a ≈ 0.385 nm is the optimum condition for a high critical temperature in high-Tc cuprates.