By the use of computer simulations we investigate, in the cellular automatonof two-dimensional traffic flow, the anisotropic effect of the probabilities ofthe change of the move directions of cars, from up to right ($p_{ur}$) and fromright to up ($p_{ru}$), on the dynamical jamming transition and velocitiesunder the periodic boundary conditions in one hand and the phase diagram underthe open boundary conditions in the other hand. However, in the former case,the first order jamming transition disappears when the cars alter theirdirections of move ($p_{ur}\neq 0$ and/or $p_{ru}\neq 0$). In the open boundaryconditions, it is found that the first order line transition between jammingand moving phases is curved. Hence, by increasing the anisotropy, the movingphase region expand as well as the contraction of the jamming phase one.Moreover, in the isotropic case, and when each car changes its direction ofmove every time steps ($p_{ru}=p_{ur}=1$), the transition from the jammingphase (or moving phase) to the maximal current one is of first order.Furthermore, the density profile decays, in the maximal current phase, with anexponent $\gamma \approx {1/4}$.}
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