  We discuss the relation between the T^{2}-coefficient of electrical
resistivity $A$ and the T-linear specific-heat coefficient $\gamma$ for
heavy-fermion systems with general $N$, where $N$ is the degeneracy of
quasi-particles. A set of experimental data reveals that the Kadowaki-Woods
relation; $A/\gamma^{2} = 1*10^{-5} {\mu\Omega}(K mol/mJ)^{2}$, collapses
remarkably for large-N systems, although this relation has been regarded to be
commonly applicable to the Fermi-liquids. Instead, based on the Fermi-liquid
theory we propose a new relation; $\tilde{A}/\tilde{\gamma}^2=1\times10^{-5}$
with $\tilde{A} = A/(1/2)N(N-1)$ and $\tilde{\gamma} = \gamma/(1/2)N(N-1)$.
This new relation exhibits an excellent agreement with the data for whole the
range of degenerate heavy-fermions.
