We present the conceptual design and initial development of the hysteretic deformable mirror (HDM). The HDM is a completely new approach to the design and operation of deformable mirrors (DMs) for wavefront correction in advanced imaging systems. The key technology breakthrough is the application of highly hysteretic piezoelectric material in combination with a simple electrode layout to efficiently define single actuator pixels. The set-and-forget nature of the HDM, which is based on the large remnant deformation of the newly developed piezomaterial, facilitates the use of time division multiplexing to address the single pixels without the need for high update frequencies to avoid pixel drift. This, in combination with the simple electrode layout, paves the way for upscaling to extremely high pixel numbers (≥128  ×  128) and pixel density (100  /  mm²) DMs, which is of great importance for high spatial frequency wavefront correction in some of the most advanced imaging systems in the world.