  We derive the reduction formula, which expresses the survival rate for the
three-flavor neutrino oscillation by the two-flavor one, to the next-to-leading
order in case there is one resonance due to the matter effect. We numerically
find that the next-to-leading reduction formula is extremely accurate and the
improvement is relevant for the precision test of solar neutrino oscillation
and the indirect measurment of CP violation in the leptonic sector. We also
derive the reduction formula, which is slightly different from that previously
obtained, in case there are two resonances. We numerically verify that this
reduction formula is quite accurate and is valid for wider parameter region
than the previously obtained ones are.
