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 is known that, as $n \to \infty$, if $n/N$ converges
to a positive number and the empirical distribution of the eigenvalues of $T_n$
converges to a proper probability distribution, then the empirical distribution
of the eigenvalues of $B_n$ converges a.s. to a nonrandom limit. In this paper
we prove that, under certain conditions on the eigenvalues of $T_n$, for any
closed interval outside the support of the limit, with probability 1 there will
be no eigenvalues in this interval for all $n$ sufficiently large.