Lorentz transformation without the direct use of Einstein`s postulates

A new derivation of the Lorentz transformation that does not directly use Einstein`s postulates, that is, the principle of relativity and the principle of the constancy of light velocity, is given. This method is based on simpler and more definite principles that consist of only the reciprocity of speed (not velocity), the independence of coordinate transformation, the homogeneity of time and space, the isotropy of space, and some additional principles. The argument stated here is important in considering a rigorous definition of the principle of relativity in depth. Besides, the relation between lines and relative velocities is discussed as lemmas.