  It is known that the normalized maxima of a sequence of independent and
identically distributed bivariate normal random vectors with correlation
coefficient $\rho \in (-1,1)$ is asymptotically independent, which may
seriously underestimate extreme probabilities in practice. By letting $\rho$
depend on the sample size and go to one with certain rate, H\"usler and Reiss
(1989) showed that the normalized maxima can become asymptotically dependent.
In this paper, we extend such a study to a triangular array of multivariate
Gaussian sequence, which further generalizes the results in Hsing, H\"usler and
Reiss (1996) and Hashorva and Weng (2013).
