  Measurement-induced nonlocality is a measure of nonlocalty introduced by Luo
and Fu [Phys. Rev. Lett \textbf{106}, 120401 (2011)]. In this paper, we study
the problem of evaluation of Measurement-induced nonlocality (MIN) for an
arbitrary $m\times n$ dimensional bipartite density matrix $\rho$ for the case
where one of its reduced density matrix, $\rho^{a}$, is degenerate (the
nondegenerate case was explained in the preceding reference). Suppose that, in
general, $\rho^{a}$ has $d$ degenerate subspaces with dimension $m_{i} (m_{i}
\leq m, i=1, 2, ..., d)$. We show that according to the degeneracy of
$\rho^{a}$, if we expand $\rho$ in a suitable basis, the evaluation of MIN for
an $m\times n$ dimensional state $\rho$, is degraded to finding the MIN in the
$m_{i}\times n$ dimensional subspaces of state $\rho$. This method can reduce
the calculations in the evaluation of MIN. Moreover, for an arbitrary $m\times
n$ state $\rho$ for which $m_{i}\leq 2$, our method leads to the exact value of
the MIN. Also, we obtain an upper bound for MIN which can improve the ones
introduced in the above mentioned reference. In the final, we explain the
evaluation of MIN for $3\times n$ dimensional states in details.
