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Tunneling electroresistance (TER) effect is the change in the electrical resistance of a ferroelectric tunnel junction (FTJ) associated with polarization reversal in the ferroelectric barrier layer. Here we predict that a FTJ with a composite barrier that combines a functional ferroelectric film and a thin layer of a nonpolar dielectric can exhibit a significantly enhanced TER. Due to the change in the electrostatic potential with polarization reversal, the nonpolar dielectric barrier acts as a switch that changes its barrier height from a low to high value. The predicted values of TER are giant and indicate that the resistance of the FTJ can be changed by several orders in magnitude at the coercive electric field of ferroelectric.