  We develop an improved method to explore the $\Xi_c- \Xi_c'$ mixing which
arises from the flavor SU(3) and heavy quark symmetry breaking. In this method,
the flavor eigenstates under the SU(3) symmetry are at first constructed and
the corresponding masses can be nonperturbatively determined. Matrix elements
of the mass operators which break the flavor SU(3) symmetry sandwiched by the
flavor eigenstates are then calculated. Diagonalizing the corresponding matrix
of Hamiltonian gives the mass eigenstates of the full Hamiltonian and
determines the mixing. Following the previous lattice QCD calculation of
$\Xi_c$ and $\Xi_c'$, and estimating an off-diagonal matrix element, we extract
the mixing angle between the $\Xi_c$ and $\Xi_c'$. Preliminary numerical
results for the mixing angle confirm the previous observation that such mixing
is incapable to explain the large SU(3) symmetry breaking in semileptonic
decays of charmed baryons.
