  In this paper, we propose a new deformed Poisson brackets which leads to the
Fock coordinate transformation by using an analogous procedure as in Deformed
Special Relativity. We therefore derive the corresponding momentum
transformation which is revealed to be different from previous results.
Contrary to the earlier version of Fock's nonlinear relativity for which plane
waves cannot be described, our resulting algebra keeps invariant for any
coordinate and momentum transformations the four dimensional contraction
$p_{\mu} x^{\mu} $, allowing therefore to associate plane waves for free
particles. As in Deformed Special Relativity, we also derive a canonical
transformation with which the new coordinates and momentum satisfy the usual
Poisson brackets and therefore transform like the usual Lorentz vectors.
Finally, we establish the dispersion relation for Fock's nonlinear relativity.
