We consider here a multivariate sample Xj = (X1.j > ... > Xi.j), 1 = j = n, where the Xj, 1 = j = n, are independent i-dimensional extremal vectors with suitable unknown location and scale parameters ? and d respectively. Being interested in linear estimation of these parameters, we consider the multivariate sample Zj, 1 = j = n, of the order statistic of largest values and their concomitants, and the best linear unbiased estimators of ? and d based on such multivariate sample. Computational problems associated to the evaluation of µi(n) and Si(n), the mean value and the covariance matrix of standardized Zj, 1 = j = n, are also discussed.