The unit root test proposed by Ranjbar et al. (2018) was examined for an alternative of stationary asymmetric exponential smooth transition autoregressive (AESTAR) under structural breaks. The situation that stands out as a deficiency in the mentioned study was that the model that does not includes the zero-mean structure not taken into account. On the contrary, the features of the zero-mean model should also had been explained. Because time-varying deterministic terms were removed from the time series for describing the structural breaks. The fact that no deterministic terms were formed due to the transformation during the redefinition of the difference equation indicates that the obtained structure should be evaluated in the model structure with zero-mean. This test methodology developed as an alternative is the interpretation of Sollis (2009) model under Fourier series that can be called Fourier-Sollis test for zero-mean model condition. The critical values in terms of finite samples were calculated and the size and power properties were evaluated. The power properties of the Fourier-Sollis and Fourier-KSS tests were compared under the assumption of symmetric/asymmetric reversions. Under the asymmetric reversions, Fourier-Sollis test was found to be more successful. However, under the symmetric assumption, these tests can be used together.