In this paper ak-sample non-parametric test for trend is considered. Given a sample of sizeni,i= 1, …,krespectively from each ofkpopulations, the test rejects the hypothesis that thekpopulations are identical ifS= Σki=2Si≥Si. Here Si is the Mann-Whitney statistic computed when each observation in thei-th sample is compared with the combined observations from the first (i– 1) populations. A recurrence formula is derived for computing the exact distribution of S. Tables of exact probabilities and critical values are given for nominal values of α = 0.5, 0.2, 0.1, 0.05, 0.025, 0.01, and 0.005 fork= 3 and all possible sample sizes from 2 to 8, and for equal sample sizes for values ofn= 2(1)6,k= 4(1)6.