The nature of the cubic-like state in the lead-free piezoelectric ceramics 0.5K0.5Na0.5NbO3-0.5Na0.5Bi0.5TiO3 (KNN-50BNT) has been examined in detail by synchrotron x-ray diffraction (SD), selected area electron diffraction (SAED), neutron diffraction (ND), and temperature dependent dielectric characterization. The SD pattern of KNN-50BNT presents a pure perovskite structure with pseudocubic symmetry. However, superlattice reflections were observed by SAED and completely indexed by tetragonal symmetry with P4bm space group in ND pattern. The relaxor behavior of KNN-50BNT is compared with Pb-based and Ba-based relaxors and discussed in the framework of the Vogel-Fulcher law and the new glass model. The KNN-50BNT ceramic exhibits the strongest dielectric dispersion among them. ; Comment: 20 pages, 4 figures, 3 tables