In several experimental studies of electron paramagnetic resonance and antiferromagnetic resonance performed on the one-dimensional Heisenberg antiferromagnet KCuF3, a Dzyaloshinsky-Moriya (DM) antisymmetric exchange interaction between spins on the c-axis was confirmed. However, the crystal symmetry with the space group D-4h(18) - I4/mcm that had been accepted then did not allow this interaction. Thus we doubted the old crystal structure. Improving the quality of single-crystal samples, we reexamine the crystal structure of KCuF3 by using an X-ray diffraction technique at room temperature. As a result, we confirm that F-atoms on the c-axis are displaced from the Cu-Cu bonding lines; which differs from the old structure. Consequently: a new superlattice structure is formed both along the c-axis and in the c-plane. On the basis of the newly found structure, we determine that the space group is D-2(4) - P2(1)2(1)2(1), and find that the local symmetry around a Cu-Cu bonding line along the c-axis allows the DM interaction with the DM vector perpendicular to the c-axis.