Consider a triangular array of stationary normal random variables
${\xi_{n, i}, i \geq 0, n \geq 1)$ such that ${\xi_{n, i}, i \geq 0}$ is a
stationary normal sequence for each $n \geq 1$. Let $\rho_{n, j} = \corr
(\xi_{n, i}, \xi_{n, i + j})$. We show that if $(1 - \rho_{n,j}) \log n \to
\delta_j \epsilon (0, \infty)$ as $n \to \infty$ for some j, then the
locations where the extreme values occur cluster, and if $\rho_{n,j}$ tends to
0 fast enough as $j \to \infty$ for fixed n, then ${\xi_{n, i}, i \geq
0}$ satisfies a certain weak dependence condition. Under the two conditions, it
is possible to speak about an index which measures the degree of clustering. In
practice, this viewpoint can provide a better approximation of the
distributions of the maxima of weakly dependent normal random variables than
what is directly guided by the asymptotic theory of Berman.