We study the observables of 158 relatively normal Type Ia supernovae (SNe Ia) by dividing them into two groups in terms of the expansion velocity inferred from the absorption minimum of the Si II 6355 line in their spectra near B-band maximum brightness. One group (Normal) consists of normal SNe Ia populating a narrow strip in the Si II velocity distribution, with an average expansion velocity v=10,600+/-400 km/s near B maximum; the other group (HV) consists of objects with higher velocities, v > 11,800 km/s. Compared with the Normal group, the HV one shows a narrower distribution in both the peak luminosity and the luminosity decline rate dm_{15}. In particular, their B-V colors at maximum brightness are found to be on average redder by ~0.1, suggesting that they either are associated with dusty environments or have intrinsically red B-V colors. The HV SNe Ia are also found to prefer a lower extinction ratio Rv~1.6 (versus ~2.4 for the Normal ones). Applying such an absorption-correction dichotomy to SNe Ia of these two groups remarkably reduces the dispersion in their peak luminosity from 0.178 mag to only 0.125 mag.
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