  The use of Type Ia supernovae (SNe Ia) as cosmological standard candles is a
key to solving the mystery of dark energy. Improving the calibration of SNe Ia
increases their power as cosmological standard candles. We find tentative
evidence for a correlation between the late-time lightcurve slope and the peak
luminosity of SNe Ia in the B band; brighter SNe Ia seem to have shallower
lightcurve slopes between 100 and 150 days from maximum light. Using a Markov
Chain Monte Carlo analysis in calibrating SNe Ia, we are able to simultaneously
take into consideration the effect of dust extinction, the luminosity and
lightcurve width correlation (parametrized by \Delta m_{15}), and the
luminosity and late-time lightcurve slope correlation. For the available sample
of 11 SNe Ia with well-measured late-time lightcurves, we find that correcting
for the correlation between luminosity and late-time lightcurve slope of the
SNe Ia leads to an intrinsic dispersion of 0.12 mag in the Hubble diagram. Our
results have significant implications for future supernova surveys aimed to
illuminate the nature of dark energy.
