  We consider transformations between uniformly accelerated systems, assuming
that the Clock Hypothesis is false. We use the proper velocity-time description
of events rather than the usual space-time description in order to obtain
linear transformations. Based on the generalized principle of relativity and
the ensuing symmetry, we obtain transformations of Lorentz-type. We predict the
existence of a maximal acceleration and time dilation due to acceleration. We
also predict a Doppler shift due to acceleration of the source in addition to
the shift due to the source's velocity. Based on our results, we explain the W.
K\"{u}ndig experiment, as reanalyzed by Kholmetski \textit{et al}, and obtain
an estimate of the maximal acceleration.
