  The problems of using the spectral index of radio galaxies in various tests,
in particular, in selecting distant radio sources are considered. The history
of the question of choosing a criterion of searching for distant radio galaxies
based on the spectral index is presented. For a new catalog of 2442 radio
galaxies constructed from NED, SDSS, and CATS data, an analytical form of the
sp ectral index.redshift relation has been determined for the first time. The
spectral index.angular size and spectral index.flux density diagrams have also
been constructed. Peculiarities of the distribution of sources on these
diagrams are discussed.
