  The universal bifurcation property of the H\'enon map in parameter space is
studied with symbolic dynamics. The universal-$L$ region is defined to
characterize the bifurcation universality. It is found that the universal-$L$
region for relative small $L$ is not restricted to very small $b$ values. These
results show that it is also a universal phenomenon that universal sequences
with short period can be found in many nonlinear dissipative systems.
