A system and method for selectively treating aberrant cells such as cancer cells through administration of a train of electrical pulses is described. The pulse length and delay between successive pulses is optimized to produce effects on intracellular membrane potentials. Therapies based on the system and method produce two treatment zones: an ablation zone surrounding the electrodes within which aberrant cells are non-selectively killed and a selective treatment zone surrounding the ablation zone within which target cells are selectively killed through effects on intracellular membrane potentials. As a result, infiltrating tumor cells within a tumor margin can be effectively treated while sparing healthy tissue. The system and method are useful for treating various cancers in which solid tumors form and have a chance of recurrence from microscopic disease surrounding the tumor.