  Koide's mass relation of charged leptons has been extended to quarks and
neutrinos, and we prove here that this relation is independent of energy scale
in a huge energy range from $1 {GeV}$ to $2\times10^{16} {GeV}$. By using the
parameters $k_u$, $k_d$ and $k_{\nu}$ to describe the deviations of quarks and
neutrinos from the exact Koide's relation, we also check the quark-lepton
complementarity of masses such as $k_{l}+k_{d} \approx k_{\nu}+k_{u} \approx
2$, and show that it is also independent (or insensitive) of energy scale.
