  Using data from the Complete Nearby ($z_{host}<0.02$) sample of Type Ia
Supernovae (CNIa0.02), we discover a linear relation between two parameters
derived from the $B-V$ color curves of Type Ia supernovae: the "color stretch"
$s_{BV}$ and the rising color slope $s_0^*(B-V)$ after the peak, and this
relation applies to the full range of $s_{BV}$. The $s_{BV}$ parameter is known
to be tightly correlated with the peak luminosity, and especially for "fast
decliners" (dim Type Ia supernovae), and the luminosity correlation with
$s_{BV}$ is markedly better than with the classic light-curve width parameters
such as $\Delta{m_{15}(B)}$. Thus our new linear relation can be used to infer
peak luminosity from $s_0^*$. Unlike $s_{BV}$ (or $\Delta{m_{15}}$), the
measurement of $s_0^*(B-V)$ does not rely on the well-determined time of
light-curve peak or color maximum, making it less demanding on the light-curve
coverage than past approaches.
