  We consider $n\times n$ random matrices $M_{n}=\sum_{\alpha =1}^{m}{\tau
_{\alpha }}\mathbf{y}_{\alpha }\otimes \mathbf{y}_{\alpha }$, where $\tau
_{\alpha }\in \mathbb{R}$, $\{\mathbf{y}_{\alpha }\}_{\alpha =1}^{m}$ are
i.i.d. isotropic random vectors of $\mathbb{R}^n$, whose components are not
necessarily independent. It was shown in arXiv:0710.1346 that if
$m,n\rightarrow \infty$, $m/n\rightarrow c\in \lbrack 0,\infty )$, the
Normalized Counting Measures of $\{\tau _{\alpha }\}_{\alpha =1}^{m}$ converge
weakly and $\{\mathbf{y}_\alpha\}_{\alpha=1}^m$ are \textit{good} (see
corresponding definition), then the Normalized Counting Measures of eigenvalues
of $M_{n}$ converge weakly in probability to a non-random limit found in
\cite{Ma-Pa:67}. In this paper we indicate a subclass of good vectors, which we
call \textit{very good} and for which the linear eigenvalue statistics of the
corresponding matrices converge in distribution to the Gaussian law, i.e., the
Central Limit Theorem is valid. An important example of good vectors, studied
in arXiv:0710.1346 are the vectors with log-concave distribution. We discuss
the conditions for them, guaranteeing the validity of the Central Limit Theorem
for linear eigenvalue statistics of corresponding matrices.
