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 2x10(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)approximate to k(nu)+k(u)approximate to 2, and show that it is also independent (or insensitive) of energy scale.
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