A driven voltage-controlled reversible electrooptic effect in a smectic A phase with a preceding twisted nematic phase or a large-pitch cholesteric phase and SiO anchoring has been discovered. The unique feature of this novel electrooptic effect in a smectic A is that it reverses by relaxing when the electric field is removed. The conditions permitting the observation of such an effect are described in detail. On the basis of the smectic A textures observed a simple topological model is given. The influence of the polyvinyl alcohol anchoring is studied in the following paper. The main advantages and disadvantages of this novel electrooptic effect for a display device are briefly discussed.