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Using data from the Complete Nearby (redshift z _host < 0.02) sample of Type Ia Supernovae (CNIa0.02), we find 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, 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 Δ m _15 ( B ). Thus, our new linear relation can be used to infer peak luminosity from ${s}_{0}^{* }$ . Unlike s _BV (or Δ m _15 ( B )), the measurement of ${s}_{0}^{* }(B-V)$ does not rely on a well-determined time of light-curve peak or color maximum, making it less demanding on the light-curve coverage than past approaches.