Summary: A three-sample distribution-free test for detecting non-decreasing ordered alternatives is proposed to alleviate some of the problems in the existing tests, including the risk of frequent detection of a trend when it is not actually present. The test is based on the natural U-statistic estimation of the parameter \(\gamma = P(Y_1 \leq Y_2 \leq Y_3)\) where \(Y_1,Y_2,Y_3\) are three independent continuous random variables. Actual levels of the test and power values in the case of equal variances for a variety of sample sizes and over a wide class of distributions under the null hypothesis and the alternative are obtained via simulation. The results indicate that the proposed test compares favorably with existing tests. In all simulations the nonparametric test provided relatively good power, accurate control over the size of the test, and better protection against false detection of a non-existing trend.