  Effects of a new triple-alpha reaction rate on the ignition of carbon-oxygen
white dwarfs accreting helium in a binary systems have been investigated. The
ignition points determine the properties of a thermonuclear explosion of a Type
Ia supernova. We examine the cases of different accretion rates of helium and
different initial masses of the white dwarf, which was studied in detail by
Nomoto. We find that for all cases from slow to intermediate accretion rates,
nuclear burnings are ignited at the helium layers. As a consequence, carbon
deflagration would be triggered for the lower accretion rate compared to that
of $dM/dt\simeq 4\times10^{-8} M_{\odot} \rm yr^{-1}$ which has been believed
to the lower limit of the accretion rate for the deflagration supernova.
  Furthermore, off-center helium detonation should result for intermediate and
slow accretion rates and the region of carbon deflagration for slow accretion
rate is disappeared.
