The article presents the original derivation method of transformations for kinematics with a universal reference system. This method allows to derive transformations that meet the results of the Michelson-Morley and Kennedy-Thorndike experiments only in some frame of reference, e.g. in laboratories moving in relation to a universal frame of reference with small speeds. These generalized transformations have been called the generalized Galilean transformations. The obtained transformations are the basis for the derivation of the new physical theory, which has been called the Special Theory of Ether. The generalized Galilean transformations can be expressed by relative speeds (26)-(27) or by the parameter delta(v) (37)-(38). Based on conclusions of the Michelson-Morley’s and Kennedy-Thorndike’s experiments, the parameter delta(v) was determined. This allows the transformations to take a special form (81)-(82), which is consistent with experiments in which velocity of light is measured. On the basis of obtained transformations, the formulas for summing speed and relative speed were also determined. The entire article includes only original research conducted by its author.