We have experimentally observed the biaxial switching between two topologically distinct textures of a nematic liquid crystal cell submitted to a strong electric field. The effect is deduced from optical and electrical measurements across the cell. Above a static threshold, a bulk order reconstruction is observed, where the final nematic orientation in the centre becomes perpendicular to its initial one, inducing a total pi change of orientation across the cell. Using short electric field pulses, a higher dynamical threshold is observed. These experiments are explained by a Landau-de Gennes-Khalatnikov model. The threshold implies the local exchange of two eigenvalues of the nematic order tensor through intermediate biaxial states. The onset of the effect in a thin splay-bend wall decreases the static threshold by almost an order of magnitude. The model explains reasonably well the static and dynamic measurements within the present description of nematic biaxiality.