Let $B _n = (1/N) T_n^{1/2} X _n X _n^*T_n^{1/2}$ where $X_n$ is $n
\times N$ with i.i.d. complex standardized entries having finite fourth moment,
and $T_n^{1/2}$ is a Hermitian square root of the nonnegative definite
Hermitian matrix $T_n$. It was shown in an earlier paper by the authors that,
under certain conditions on the eigenvalues of $T_n$, with probability 1 no
eigenvalues lie in any interval which is outside the support of the limiting
empirical distribution (known to exist) for all large $n$. For these $n$ the
interval corresponds to one that separates the eigenvalues of $T_n$. The aim of
the present paper is to prove exact separation of eigenvalues; that is, with
probability 1, the number of eigenvalues of $B_n$ and $T_n$ lying on one side
of their respective intervals are identical for all large $n$.