The phase diagram of the lead-free piezoelectric (1 − x)K_0.5Na_0.5NbO₃–xBi_1/2Na_1/2TiO₃ system has been studied by high-resolution synchrotron powder diffraction, neutron powder diffraction and selected area electron diffraction. The two lead-free piezoelectric materials K_0.5Na_0.5NbO₃ and Bi_1/2Na_1/2TiO₃ form an infinite substitution solid solution. The orthorhombic (O), monoclinic (M), tetragonal (T) and rhombohedral (R) phases and the phase coexistence of M (Pm) + T (P4mm) for 0.02 < x ≤ 0.14, T (P4bm) + pseudocubic (Pm{\overline 3}m) for 0.14 < x ≤ 0.87 and T (P4bm) + R (R3c) for 0.87 < x ≤ 0.96 have been investigated at room temperature, with a subtle change in the structure observed. The oxygen octahedral tilt system has been mapped as a function of composition and temperature. The results indicate that K_0.5Na_0.5NbO₃–Bi_1/2Na_1/2TiO₃ does not display a morphotropic phase boundary like lead zirconate titanate, and that the most significant structural changes as a function of composition occur near x = 0.14 and x = 0.87 as a result of ionic disorder at the A and B sites in the perovskite ABO₃ structure at room temperature.