  Statistical connections between the properties of Type Ia supernovae (SNe Ia)
and the B--V colors of their parent galaxies are established. Compared to SNe
Ia in blue galaxies [B-V$\la$0.75], SNe Ia in redder galaxies have (1) a wider
dispersion in the blueshifts of their Si II $\lambda$6355 absorption features,
ten days after maximum light; (2) more rapidly declining light curves; and (3)
lower luminosities. Even when the spectroscopically peculiar, very subluminous
SNe Ia such as SN 1991bg are disregarded, SNe Ia in red galaxies are less
luminous than those in blue galaxies by about 0.3 magnitudes.
  When SNe Ia that are thought to have been significantly extinguished by dust
in their parent galaxies are disregarded, those in blue galaxies have
observational absolute--magnitude dispersions of only $\sigma_{obs}(M_B)$=0.20
and $\sigma_{obs}(M_V)$=0.17, which implies that their intrinsic
absolute--magnitude dispersions are very small. We use six SNe Ia whose
absolute magnitudes have been calibrated by means of Cepheids, which also
indicate that the intrinsic absolute--magnitude dispersions of SNe Ia in blue
galaxies are very small, to calibrate SNe Ia in blue galaxies and obtain $\rm
H_0=57\pm4\ km\ s^{-1}\ Mpc^{-1}$. This value is in excellent agreement with
that obtained by Saha et al. (1995b), in spite of the fact that they do not
take into account any dependence of SN Ia absolute magnitude on the nature of
the parent galaxy.
  Some implications of the statistical connections between SNe Ia and the
colors of their parent galaxies, for identifying the progenitor binary systems
of SNe Ia and for using high--redshift SNe Ia to measure q$_0$, are briefly
discussed.
