Dynamical critical exponents for the four dimensional Ising model are Computed on a cellular automaton from the relaxations of the time displaced correlation for the order parameter and the internal energy at the critical temperatures. The analysis of the data within the frame of the dynamical finite-size scaling hypothesis gives the linear dynamical critical exponents for the order parameter and the internal energy. In our calculation, the linear dynamical critical exponents are found z(M) = z(HI) = 2.04 at T-c(infinity), z(M) = 1.99, z(HI) = 2.00 at T-c(chi)(L). The values of Z(M) = Z(HI) = 2.04 obtained for T-c(infinity) verify the dynamical finite-size scaling, for which it was adopted four dimensional Ising model. (c) 2005 Elsevier B.V. All rights reserved.