We report on the discovery of an isothermal structural transition observed in Bi 1−x La x FeO 3 (0.17 x 0.19) ceramics. At room temperature, an initially pure polar rhombohedral phase gradually transforms into a pure antipolar orthorhombic one. The polar phase can be recovered by annealing at T > 300 • C. In accordance with neutron powder diffraction data, an inverse isothermal antipolar-polar transition takes place at T > 300 • C, where the polar phase becomes more stable. The antipolar phase is characterized by a weak ferromagnetic state, whereas the polar phase has been obtained in a mixed antiferromagnet-weak ferromagnet state. The relatively low external pressure induces polar-antipolar transition, but there is no evidence of electric-field-driven antipolar-polar transition. The observed large local piezoelectric response is associated with structural instability of the polar phase, whereas local multistate piezoelectric loops can be related to the domain wall pinning effect.