The generalized Møller-Wu-Lee transformations are derived for constant-linear-acceleration frames by using Wu's idea of a kinematic approach in flat space based on a new limiting 4-dimensional symmetry, i.e., an accelerated transformation must reduce to the 4-dimensional symmetry form of the Lorentz transformation in the limit of zero acceleration. The indicates an important departure from the result of the equivalence principle at high energies when the initial velocity β0 is large: Namely, we obtain (goo^(1/2) - 1) = γ0 ax/c^2, which involves an extra factor γ0 = (1 - ,β0^2)^(-1/2). Some physical implications and a test of the prediction for the accelerated lifetime dilation at high energies are discussed.