In this paper we propose that the velocity in the Lorentz transformation ( LT ) equations and special relativity can only be instantaneous relative velocity between inertial reference frames. We will see that this interpretation will resolve the twin paradox and lead to a deeper understanding of inertial and non-inertial reference frames. Physicists failed to note that if the travelling twin suddenly decelerated from relativistic velocity to low velocity, all space and time coordinates and separations / intervals of events will also change suddenly, retroactively, in such a way as if the travelling twin had always been travelling at that low velocity. When the travelling twin returns to Earth and comes to rest relative to the stationary twin, all ‘memory’ of his/her past relativistic journey will be lost and time intervals of events will also change retroactively as if he/she had always been at rest relative to the stationary twin, as if he had never travelled at relativistic speeds. Only instantaneous velocity is relevant and all motion history of the twin is irrelevant in the Lorentz transformations. Therefore, the problem is symmetrical with respect to both twins. Intuitive and inconsistent application of time dilation (and length contraction), rather than rigorous and consistent application of Lorentz coordinate transformation of events, has caused the creation and persistence of the twin paradox. Lorentz transformation is fundamentally about coordinate transformation of events and time dilation and length contraction are only consequences of LT. The twin paradox is a result of a somehow mixed ( relativistic and classical) views of time.