We present the results of a new, comprehensive investigation of the ra
dio spectral index of the Crab Nebula supernova remnant. New data at 7
4 MHz are combined with data at 327 MHz, 1.5 GHz, and 5 GHz. In contra
st to previous claims, little spatial Variation in the spectral index
is seen. In particular, between 327 MHz and 5 GHz we see no evidence o
f spectral steepening near the edge of the Nebula, the ''jet,'' or the
ionized filaments. The rms limits on any spectral index variations in
these regions amount to no more than 0.01. We believe that earlier re
ports of large steepening were the result of correlator bias and image
registration problems. An elongated feature was detected 1' northwest
of the pulsar, which may be a continuation of the well-known wisplike
structures seen closer to the center of the Nebula. At 74 MHz, we see
for the first time evidence of free-free absorption by the thermal ma
terial in the Crab Nebula's filaments. Apart from some possible renewe
d acceleration occurring in the wisps, the dominant accelerator of rel
ativistic electrons in the Crab Nebula is the pulsar itself.