Suppose X1, X2, , Xn is a random sample from the Np(θ, V) distribution. Consider H0: θ1 = θ2 = = θp = 0 and H1: θi>0 for i = 1, 2, , p, let H1-H0 denote the hypothesis that H1 holds but H0 does not and let~H0 denote the hypothesis that H0 does not hold. Because the Likelihood Ratio Test (LRT) of H0 versus H1-H0 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.