  The Wolfenstein parametrization of the $3\times 3$ Kobayashi-Maskawa (KM)
matrix $V$ is modified by keeping its unitarity up to the accuracy of
$O(\lambda^{6})$. This modification can self-consistently lead to the
off-diagonal asymmetry of $V$: $|V_{ij}|^{2}-|V_{ji}|^{2}$ =
$Z\displaystyle\sum_{k}\epsilon^{~}_{ijk}$ with $Z=\approx A^{2}\lambda^{6}
(1-2\rho)$, which is comparable in magnitude with the Jarlskog parameter of
$CP$ violation $J\approx A^{2}\lambda^{6}\eta$. We constrain the ranges of $J$
and $Z$ by using the current experimental data, and point out that the
possibility of a symmetric KM matrix has almost been ruled out.
