  As a promising channel to Type Ia supernovae (SNe Ia), we have proposed a
symbiotic binary system consisting of a white dwarf (WD) and a low mass
red-giant (RG), where strong winds from the accreting WD play a key role to
increase the WD mass to the Chandrasekhar mass limit. Here we propose two new
evolutionary processes which make the symbiotic channel to SNe Ia much wider.
(1) We first show that the WD + RG close binary can form from a wide binary
even with such a large initial separation as $a_i \lesssim 40000 R_\odot$. Such
a binary consists of an AGB star and a low mass main-sequence (MS) star, where
the AGB star is undergoing superwind before becoming a WD. If the superwind at
the end of AGB evolution is as fast as or slower than the orbital velocity, the
wind outflowing from the system takes away the orbital angular momentum
effectively. As a result the wide binary shrinks greatly to become a close
binary. Therefore, the WD + RG binary can form from much wider binaries than
our earlier estimate. (2) When the RG fills its inner critical Roche lobe, the
WD undergoes rapid mass accretion and blows a strong optically thick wind. Our
earlier analysis has shown that the mass transfer is stabilized by this wind
only when the mass ratio of RG/WD is smaller than 1.15. Our new finding is that
the WD wind can strip mass from the RG envelope, which could be efficient
enough to stabilize the mass transfer even if the RG/WD mass ratio exceeds
1.15. With the above two new effects (1) and (2), the symbiotic channel can
account for the inferred rate of SNe Ia in our Galaxy.
