Here I report on how Fourier Transform Electrochemical Impedance Spectroscopy (FTEIS) overcomes the potential-current linearity problem encountered in the impedance calculation process. FTEIS was first invented to solve the time-related drawback of the conventional impedance technique. The dramatic time reduction of FTEIS enabled the real-time impedance measurement but brought about the linearity problem at the same time. While the conventional method circumvents the problem using the steady-state made by a sufficiently long measurement time, FTEIS cannot because of its real-time function. However, according to the mathematical development reported in this article, the potential step used in FTEIS is proved to avoid the linearity problem. During the step period, the potential and the current are linearized by the electrochemical impedance. Also, Fourier transform of the differentiated potential and current is proved to give the same result of the original ones.