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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 theoff-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 thepossibility of a symmetric KM matrix has almost been ruled out.Comment: 5 Latex pages including a figure; Two references are adde

Wolfenstein parametrization reexamined