The initial radiation fields, Poynting vector, and total electromagnetic power that a vertical return stroke radiates into the upper half space have been computed when the speed of the stroke, &ngr;, is a significant fraction of the speed of light, c, assuming that at large distances and early times the source is an infinitesimal dipole. The initial current is also assumed to satisfy the transmission-line model with a constant &ngr; and to be perpendicular to an infinite, perfectly conducting ground. The effect of a large &ngr; is to increase the radiation fields by a factor of (1-β2 cos2 &thgr;)-1, where β=&ngr;/c and &thgr; is measured from the vertical, and the Poynting vector by a factor of (1-β2 cos2 &thgr;)-2. This increase is just a few percent or less at small β, but when β=0.67, the fields are about 80% larger at small &thgr; and 50% larger at &thgr;=30¿, and the power that is radiated is increased by 26%. When β=0.5 and the peak current is 30 kA, typical values for negative first strokes, the peak power that is radiated into the upper hemisphere is 1.0¿1010 W. ¿ American Geophysical Union 1992