A new method for the ablation of undesirable tissue such as cells of a cancerous or non-cancerous tumor is disclosed. It involves the placement of electrodes into or near the vicinity of the undesirable tissue through the application of electrical pulses causing irreversible electroporation of the cells throughout the entire area of the undesirable tissue. The electric pulses irreversibly permeate the cell membranes, thereby invoking cell death. The irreversibly permeabilized cells are left in situ and are removed by the body immune system. The amount of tissue ablation achievable through the use of irreversible electroporation without inducing thermal damage is considerable.