There are two versions of time dilation in Einstein’s original paper on special relativity theory (SRT). It is pointed out that they differ in a crucial respect, namely whether the phenomenon is symmetric or asymmetric. The Clock Paradox arises from belief in the latter version, which asserts that a clock runs slower when it is accelerated than an identical clock that remains at rest in its initial rest frame. The symmetric theory of time dilation is based on the Lorentz invariance condition of the Lorentz transformation (LT). Experiments have invariably shown that it is always possible to know which of two clocks is running slower, and therefore have confirmed Einstein’s asymmetric version of time dilation. The question is therefore considered whether the lengths of accelerated objects are properly described by the LT, despite the fact that it fails to predict the observed asymmetry in clock rates. The present work calls attention to the fact that Einstein’s derivation of the LT is based on an undeclared assumption in addition to his two postulates of relativity. It is shown that assuming instead that clock rates are strictly proportional to one another leads to a different version of the Lorentz transformation that still satisfies the two postulates of relativity and the velocity transformation of SRT while successfully describing the asymmetric character of time dilation.