In this paper I use the fictional Absolute inertial reference frame and Absolute Newtonian Time together with the Newton's second law for motion and the constancy of the speed of light in vacuum to find a relationship between the Newtonian Time and Einstein Time. Using this relationship as the stepping stone I then construct a set of relativistic transformation equations between two realistic non-newtonian inertial reference frames associated with Einstein Time. These transformation equations lead to some very interesting consequences such as: (1) There is no upper limit on the relative speed of a moving inertial reference frame with respect to a "stationary" inertial reference frame, (2) There is no length contraction in the moving frame, (3) There is time dilation in the moving frame that is qualitatively similar to Einstein's Special Theory of Relativity, (4) Supra-luminal relative speeds are allowed for the moving reference frame, (5) With supra-luminal relative speed of moving frame the Einstein Time in it moves backwards, (6) The mass/energy relation of Einstein is preserved, (7) Current and as yet unexplainable cosmic and quantum mechanical events can be used to see if the theory is able to explain them. After this the theory can be used to prediction as yet unknown phenomenon.