  We find finite-boost transformations DSR theories in first order of the
Planck length $l_p$, by solving differential equations for the modified
generators. We obtain corresponding dispersion relations for these
transformations, which help us classify the DSR theories via four types. The
final type of our classification has the same special relativistic dispersion
relation but the transformations are not Lorentz. In DSR theories, the velocity
of photons is generally different from the ordinary speed c and possess time
delay, however in this new DSR light has the same special relativistic speed
with no delay. A special case demonstrates that any search for quantum gravity
effects in observations which gives a special relativistic dispersion relation
is consistent with DSR.
