Effects of a new triple-a 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 la 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 ≃4 × 10-8M⊙ 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.