The fundamental property of most single-electron devices with quasicontinuous quasiparticle spectrum on the island is the periodicity of their transport characteristics in the gate voltage. This property is robust even with respect to placing the ferroelectric insulators in the source and drain tunnel junctions. We show that placing the ferroelectric inside the gate capacitance breaks this periodicity. The current-voltage characteristics of this SET strongly depends on the ferroelectric polarization and shows the giant memory-effect even for negligible ferroelectric hysteresis making this device promising for memory applications.