Recent observations of terrestrial gamma-ray flashes (TGFs) (Smith et al., 2005) suggest the need for a new mechanism of TGF production. Consideration of relativistic runaway electron (RRE) avalanche driven by electromagnetic impulses (EMP) radiated by rapidly moving lightning return strokes indicates that TGFs can be produced by discharges with peak return stroke currents Ip > 450--700 kA with velocities vrs/c = 0.99--0.995.