We have found a new evolutionary path to Type Ia supernovae (SNe Ia) that h
as been overlooked in previous work. In this scenario, a carbon-oxygen whit
e dwarf (C+O WD) is originated not from an asymptotic giant branch star wit
h a C+O core but from a red giant star with a helium core of similar to 0.8
-2.0 M.. The helium star, which is formed after the first common envelope e
volution, evolves to form a C+O WD of similar to 0.8-1.1 M., transferring a
part of the helium envelope onto the secondary main-sequence star. This ne
w evolutionary path, together with the optically thick wind from mass-accre
ting white dwarf, provides a much wider channel to SNe Ia than previous sce
narios. A part of the progenitor systems are identified as luminous superso
ft X-ray sources or recurrent novae such as U Sco, which are characterized
by the accretion of helium-rich matter. The white dwarf accretes hydrogen-r
ich, helium-enhanced matter from a lobe-filling, slightly evolved companion
at a critical rate and blows excess matter into the wind. The white dwarf
grows in mass to the Chandrasekhar mass limit and explodes as an SN Ia. A t
heoretical 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
10 times larger than the previous theoretical estimates for white dwarfs wi
th slightly evolved companions.