  We investigate parametric decay instability (PDI) of circularly polarized
Alfv\'en wave into daughter acoustic wave and backward Alfv\'en wave in
magnetically-dominated plasma, in which the magnetization parameter $\sigma$
(energy density ratio of background magnetic field to matter) exceeds unity. We
analyze relativistic magnetohydrodynamics (MHD), focusing on wave frequencies
sufficiently lower than the plasma and cyclotron frequencies. We derive
analytical formulae for the dispersion relation and growth rate of the
instability as a function of the magnetization $\sigma$, wave amplitude $\eta$,
and plasma temperature $\theta$. We find that PDI persists even in high
magnetization $\sigma$, albeit with a decreased growth rate up to
$\sigma\to\infty$. Our formulae are useful for estimating the decay of Alfv\'en
wave into acoustic wave and heat in high magnetization $\sigma$ plasma, which
is a ubiquitous phenomenon such as in pulsars, magnetars, and fast radio
bursts.
