  We have found a new evolutionary path to Type Ia supernovae (SNe Ia) which
has been overlooked in previous work. In this scenario, a carbon-oxygen white
dwarf (C+O WD) is originated, not from an asymptotic giant branch star with a
C+O core, but from a red-giant star with a helium core of $\sim 0.8-2.0
M_\odot$. The helium star, which is formed after the first common envelope
evolution, evolves to form a C+O WD of $\sim 0.8-1.1 M_\odot$ with transferring
a part of the helium envelope onto the secondary main-sequence star. This new
evolutionary path, together with the optically thick wind from mass-accreting
white dwarf, provides a much wider channel to SNe Ia than previous scenarios. A
part of the progenitor systems are identified as the luminous supersoft X-ray
sources or the recurrent novae like U Sco, which are characterized by the
accretion of helium-rich matter. The white dwarf accretes hydrogen-rich,
helium-enhanced matter from a lobe-filling, slightly evolved companion at a
critical rate and blows excess matter in the wind. The white dwarf grows in
mass to the Chandrasekhar mass limit and explodes as an SN Ia. A theoretical
estimate indicates that this channel contributes a considerable part of the
inferred rate of SNe Ia in our Galaxy, i.e., the rate is about ten times larger
than the previous theoretical estimates for white dwarfs with slightly evolved
companions.
