Abstract: In the framework of special relativity, it is first proved that the space-time transformation between two inertial coordinate systems is surely linear if the space-time interval keeps invariant in all inertial coordinate systems. It is demonstrated that this space-time transformation is unique yet; it is finally justified that the unique space-time transformation is certainly Lorentz transformation. Therefore, the Lorentz transformation can he established according to the condition of that space-time interval keeping invariant. In the last part of this paper, it is proved that the condition of that space-time interval keeping invariant is the most basic condition of establishing Lorentz transformation, there are not any conditions which can establish Lorentz transformation as well as.

Key words: invariant of space-time interval, linearity, uniqueness, Lorentz transformation, basic condition