We propose a new nonparametric test based on the rank difference between the paired sample for testing the equality of the marginal distributions from a bivariate distribution. We also consider a modification of the novel nonparametric test based on the test proposed by Baumgartern, Weiβ, and Schindler (1998). An extensive numerical power comparison for various parametric and nonparametric tests was conducted under a wide range of bivariate distributions for small sample sizes. The two new nonparametric tests have comparable power to the paired t test for the data simulated from bivariate normal distributions, and are generally more powerful than the paired t test and other commonly used nonparametric tests in several important bivariate distributions.