An explicit procedure for generating multivariate normal random vector is presented. Using a lower triangular matrix L decomposed from the convariance matrix Σ by the CHOLESKY method, the algorithm of the generator consists of the transformation of a p-dimensional Standard normal variate z, elements of which are obtained by the Box-Muller procedure, into a p-dimensional normal random sample x=Lz+Σm from the distribution X~N(m,Σ). The efficiency of the proposed procedure is exhibited by a Monte Carlo test of the algorithm which showed that the generator is highly reliable Key Words: Multivariate random vector generation, Cholesky, decomposition, Monte Carlo simulation