The null hypothesis of short memory stationarity, is given a recommended a rank-test. The test statistic is a modified version of the popular KPSS statistic which has been suggested for the level-stationarity hypothesis wherein the original observations are replaced by ranks substitute. The rank KPSS statistic has been shown to contribute to the alike restrictive allocation as the model KPSS statistic. The unchanged rank KPSS is then employed for the trend-stationarity hypothesis, statistic to the residuals of a Theil–Sen regression on a linear trend. The asymptotic allocation of the Theil–Sen estimator are derived and it was demonstrated that the Theil–Sen detrended rank KPSS statistic seems to share the equal weak limit as the least-squares detrended KPSS. The asymptotic relative efficiency of the test is compared to the KPSS and it is shown that it may have unrestrained effectiveness gains under fat-tailed allocation remunerated by very restrained effectiveness losses under thin-tailed distributions, which further makes sure that the rank KPSS test is an apt choice to the KPSS for the major practical economic and financial utility. The feeble convergence results and asymptotic representations are expected to intrigue larger addressees as compared to those concerned with stationarity testing, which is owing to the fact that invariance principles are extensively applied in unit-root econometrics.