The decresing residual extropy (DRE) aging property was presented most recently. The significance of DRE aging property in reliability is that the uncertainty of one component is decresing during use. The main topic of this paper is how to test whether one random variable is DRE or not. First of all, we define a stochastic order to compare the strength of DRE property between two random variables. Based on this point, a parameter is derived to measure the DRE property. With the help of the related knowledge of kernel density estimation, we construct an asymptotic unbiased $U$-statistic to estimate the parameter. We accept the DRE hypothesis when the test statistic is too large. To get the asymptotic critical value of the test, the asymptotic normality of the asymptotic unbiased $U$-statistic is proved. Finally, we derive the optimal form of the kernel density estimation, and proceed the numerical simulation.