  We compute the remaining amounts of hydrogen in red giant donors to see
whether the conflict between theory and observations can be overcome. By
considering the mass-stripping effect from an optically thick wind and the
effect of thermally unstable disk, we systematically carried out binary
evolution calculation for WD + MS and WD + RG systems. Here, we focus on the
evolution of WD + RG systems. We found that some donor stars at the time of the
supernova explosion contain little hydrogen-rich material on top of the helium
core (as low as 0.017 $M_{\odot}$), which is smaller than the upper limit to
the amount derived from observations of material stripped-off by explosion
ejecta. Thus, no hydrogen line is expected in the nebular spectra of these SN
Ia. We also derive the distributions of the envelope mass and the core mass of
the companions from WD + RG channel at the moment of a supernova explosion by
adopting a binary population synthesis approach. We rarely find a RG companion
with a very low-mass envelope. Furthermore, our models imply that the remnant
of the WD + RG channel emerging after the supernova explosion is a single
low-mass white dwarf (0.15 $M_{\odot}$ - 0.30 $M_{\odot}$). The absence of a
hydrogen line in nebular spectra of SNe Ia provides support to the proposal
that the WD + RG system is the progenitor of SNe Ia.
