The article presents a new test to check if paired observations are independent, without assuming any specific distribution. The test uses a statistic called D to measure the rank differences in each pair of observations. It is similar to the Kruskal-Wallis H-test for samples of 2. The study discusses various applications of this test and its properties under the null hypothesis, including exact sampling distributions and moment coefficients. The test's large-sample theory helps in describing alternative hypotheses, approximating power, and determining sample size.