  We extended our formulation of causal dissipative hydrodynamics [T. Koide
\textit{et al.}, Phys. Rev. \textbf{C75}, 034909 (2007)] to be applicable to
the ultra-relativistic regime by considering the extensiveness of irreversible
currents. The new equation has a non-linear term which suppresses the effect of
viscosity. We found that such a term is necessary to guarantee the positive
definiteness of the inertia term and stabilize numerical calculations in
ultra-relativistic initial conditions. Because of the suppression of the
viscosity, the behavior of the fluid is more close to that of the ideal fluid.
Our result is essentially same as that from the extended irreversible
thermodynamics, but is different from the Israel-Stewart theory. A possible
origin of the difference is discussed.
