This paper discusses the unit root test against the globally stationary ESTAR model when partial stationarity is unknown and a modified Wald-type test is proposed. By simulating to tabulate the critical value, the asymptotic distributions of the test statistics are derived and the properties under finite samples are examined. In a Monte Carlo study, the test statistics show good inspection level and high inspection effects. Furthermore, compared with the popular KSS-type test proposed by Kapetanios et Al., this modified Wald-type model examines the statistics with higher inspection effects by simulating under the non-linear ESTAR model with whole stationarity.