  A parametrization of the $3\times 3$ Cabibbo-Kobayashi-Maskawa matrix, $V$,
is presented in which the parameters are the eigenvalues and the components of
its eigenvectors. In this parametrization, the small departure of the
experimentally determined $V$ from being moduli symmetric (i.e.
$|V_{ij}|=|V_{ji}|$) is controlled by the small difference between two of the
eigenvalues. In case, any two eigenvalues are equal, one obtains a moduli
symmetric $V$ depending on only three parameters. Our parametrization gives
very good fits to the available data including CP-violation. Our value of $\sin
2\beta\approx 0.7$ and other parameters associated with the ` unitarity
triangle' $V_{11}V_{13}^{*}+V_{21}V_{23}^{*}V_{31}V_{33}^{*}=0$ are in good
agreement with data and other analyses.
