  Because of flux conservation, flux-averaging {\it justifies} the use of the
distance-redshift relation for a smooth universe in the analysis of type Ia
supernova (SN Ia) data. We have combined the SN Ia data from the High-$z$ SN
Search and the Supernova Cosmology Project, and binned the combined data by
flux-averaging in redshift intervals of $\Delta z=0.05$ and $\Delta z=0.1$. We
find that the unbinned data yield a Hubble constant of $H_0=65\pm 1 $km$
$s$^{-1} $Mpc$^{-1}$ (statistical error only), a matter density fraction of
$\Omega_m=0.7\pm0.4$, and a vacuum energy density fraction of
$\Omega_{\Lambda}=1.2\pm0.5$. The binned data for $\Delta z=0.1$ yield
$H_0=65\pm 1 $km$ $s$^{-1} $Mpc$^{-1}$ (statistical error only),
$\Omega_m=0.3\pm0.6$, and $\Omega_{\Lambda}=0.7\pm0.7$. Our results are not
sensitive to the redshift bin size. Flux-averaging leads to less biased
estimates of the cosmological parameters by reducing the bias due to systematic
effects such as weak lensing.
  Comparison of the data of 18 SNe Ia published by both groups yields a mean SN
Ia peak absolute magnitude of $M_B=-19.33\pm 0.25$. The internal dispersion of
each data set is about 0.20 magnitude in the {\it calibrated} SN Ia peak
absolute magnitudes. The difference in analysis techniques introduces an
additional uncertainty of about 0.15 magnitude.
  If the SNe Ia peak absolute luminosity changes with redshift due to
evolution, our ability to measure the cosmological parameters from SN Ia data
will be significantly diminished.
