When calculating frequency-domain near fields by
the FDTD method, almost 50 % reduction in memory and
CPU operations can be achieved if only E-fields are stored
during the main time-stepping loop and H-fields computed
later. An improved method of obtaining the H-fields from
Faraday's Law is presented and shown to be orders of
magnitude more accurate than the straightforward approach,
at no additional cost. The method is validated by comparison
with analytical solution of a traveling wave, and on simulations
of dipole and patch antennas.