  We formulate a perturbative framework for the flavor transformation of the
standard three active neutrinos but with non-unitary flavor mixing matrix, a
system which may be relevant for leptonic unitarity test. We use the $\alpha$
parametrization of the non-unitary matrix and take its elements $\alpha_{\beta
\gamma}$ ($\beta,\gamma = e,\mu,\tau$) and the ratio $\epsilon \simeq \Delta
m^2_{21} / \Delta m^2_{31}$ as the small expansion parameters. Qualitatively
new two features that hold in all the oscillation channels are uncovered in the
probability formula obtained to first order in the expansion: (1) The phases of
the complex $\alpha$ elements always come in into the observable in the
particular combination with the $\nu$SM CP phase $\delta$ in the form $[e^{- i
\delta } \bar{\alpha}_{\mu e}, ~e^{ - i \delta} \bar{\alpha}_{\tau e},
~\bar{\alpha}_{\tau \mu}]$ under the PDG convention of unitary $\nu$SM mixing
matrix. (2) The diagonal $\alpha$ parameters appear in particular combinations
$\left( a/b - 1 \right) \alpha_{ee} + \alpha_{\mu \mu}$ and $\alpha_{\mu \mu} -
\alpha_{\tau \tau}$, where $a$ and $b$ denote, respectively, the matter
potential due to CC and NC reactions. This property holds only in the unitary
evolution part of the probability, and there is no such feature in the genuine
non-unitary part, while the $\delta$ - $\alpha$ parameter phase correlation
exists for both. The reason for such remarkable stability of the phase
correlation is discussed.
