We calculate the decay branching fractions of the Higgs boson to and via the charm-quark fragmentation mechanism for the color-singlet and color-octet states in the framework of non-relativistic QCD. The decay rates are governed by the charm-quark Yukawa coupling, unlike the decay , which is dominated by the - mixing. We find that the decay branching fractions can be about for , and for . We comment on the perspective of searching for the Higgs boson to transition at the High-Luminosity LHC for testing the charm-quark Yukawa coupling.