In this paper a k-sample non-parametric test for trend is considered. Given a sample of size ni , i = 1, …, k respectively from each of k populations, the test rejects the hypothesis that the k populations are identical if S = Σ k i=2 Si ≥ Si . Here Si is the Mann-Whitney statistic computed when each observation in the i-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 for k = 3 and all possible sample sizes from 2 to 8, and for equal sample sizes for values of n = 2(1)6, k = 4(1)6.