It　is　known　that　the　normalized　maxima　of　a　sequence　of　independent　and　identically　distributed　bivariate　normal　random　vectors　with　correlation　coefficient　ρ.　∈.　[-.　1,　1)　is　asymptotically　independent,　which　implies　that　using　bivariate　normal　distribution　will　seriously　underestimate　extreme　co-movement　in　practice.　By　letting　ρ　depend　on　the　sample　size　and　go　to　one　with　certain　rate,　Hüsler　and　Reiss　(1989)　showed　that　the　normalized　maxima　of　Gaussian　random　vectors　can　become　asymptotically　dependent　so　as　to　well　predict　the　co-movement　observed　in　the　market.　In　this　paper,　we　extend　such　a　study　to　a　triangular　array　of　a　multivariate　Gaussian　sequence,　which　further　generalizes　the　results　in　Hsing　etal.　(1996)　and　Hashorva　and　Weng　(2013).　©　2015　Elsevier　B.V.