Using data from the Complete Nearby (redshift zhost < 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 sBV and the rising color slope after the peak, and this relation applies to the full range of sBV. The sBV parameter is known to be tightly correlated with the peak luminosity, especially for fast decliners (dim Type Ia supernovae), and the luminosity correlation with sBV is markedly better than with the classic light-curve width parameters such as Δm15(B). Thus, our new linear relation can be used to infer peak luminosity from . Unlike sBV (or Δm15(B)), the measurement of 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.