  In a previous paper, we gave a new theoretical framework in which three
neutrino mixing in matter are discussed. Rigorous analytical solutions are
obtained. In present paper an approximate method is developed for studying
three flavor neutrino oscillations in matter in the new framework. Using
condition of $\Delta m_{1}^{2}\ll \Delta m_{2}^{2}$, decoupled resonances,
which is discovered by Kuo {\it et al.} previously, are obtained without small
angle approximation. Calculation and approximation is consistent and rigorous.
All the formulae appear in simple symmetric form and some physical
characteristic are more explicit. Around the two resonant points, the mass
eigenvalue whose eigenfunction does not take part in the oscillation process,
can be easily calculated to higher precision. We find, the oscillation
amplitude is dominated by vacuum mixing and is smaller than 1 for smaller A
resonance, but it is not in the larger A. This is characteristic for the three
flavor oscillations, but do not exist in two flavor.
