  The prospects for measuring the branching fraction of $H \to \mu ^+ \mu ^-$
at the International Linear Collider (ILC) have been evaluated based on a full
detector simulation of the International Large Detector (ILD) concept,
considering centre-of-mass energies ($\sqrt{s}$) of 250 GeV and 500 GeV. For
both $\sqrt{s}$ cases, the two final states $e^+ e^- \to q\overline{q}H$ and
$e^+ e^- \to \nu \overline{\nu}H$ have been analyzed. For integrated
luminosities of 2 ab$^{-1}$ at $\sqrt{s} = 250$ GeV and 4 ab$^{-1}$ at
$\sqrt{s} = 500$ GeV, the combined precision on the branching fraction of $H
\to \mu ^+ \mu ^-$ is estimated to be 17{\%}. The impact of the transverse
momentum resolution for this analysis is also studied.
