_{1}, X

_{2}, …, X

_{n}is a random sample from the N

_{p}(θ, V) distribution. Consider H

_{0}: θ

_{1}= θ

_{2}= … = θ

_{p}= 0 and H

_{1}: θ

_{i}>0 for i = 1, 2, …, p, let H

_{1}-H

_{0}denote the hypothesis that H

_{1}holds but H

_{0}does not and let~H

_{0}denote the hypothesis that H

_{0}does not hold. Because the Likelihood Ratio Test (LRT) of H

_{0}versus H

_{1}-H

_{0}is complicated, several ad hoc tests have been proposed. The proposed test is a permutation and scale invariant test statistic which includes information about the correlation structure in the sum of the sample mean. The simulation study showed that it maintain type I error rate level very well and it also give good powers. The proposed test also is compared with the existing one with these invariance properties.]]>