  We derive finite boost transformations based on the Lorentz sector of the
bicross-product-basis $\kappa$-Poincare' Hopf albegra. We emphasize the role of
these boost transformations in a recently-proposed new relativistic theory. We
find that when the (dimensionful) deformation parameter is identified with the
Planck length, which together with the speed-of-light constant has the status
of observer-independent scale in the new relativistic theory, the deformed
boosts saturate at the value of momentum that corresponds to the inverse of the
Planck length.
