We propose a distribution-free test, which has two main purposes. First, the test can assist in alleviating some of the problems that existing tests have with higher powers when the assumed a priori ordering among the parameters is incorrect. Second, the new test can detect the monotone trends (non-decreasing ordered and non-increasing ordered) with only one derived process. Here we propose a new test, which combines and orders all observations from least to greatest; the approximate distribution of Fourier coefficients is utilized and tests whether the location parameters are serially non-decreasing or non-increasing with the groups. Utilizing the Monte Carlo simulation, we show that the proposed test is a significant improvement over the Terpstra and Magel test [Terpstra, J. T. and Magel, R. C., “A New Nonparametric Test for the Ordered Alternative Problem,” Nonparametric Stat., Vol. 15, 2003, pp. 289–301], that is, decreasing more powers for the situation when an investigator falsely assumes an a priori ordering relationship.