  In this paper we investigate the prospects for measuring the branching
fraction of the Standard Model Higgs boson decay into a pair of $Z$ bosons at
the future Compact Linear Collider (CLIC) at 350 GeV and 3 TeV centre-of-mass
energies. Studies are performed using a detailed simulation of the detector for
CLIC, taking into consideration all relevant physics and beam-induced
background processes. It is shown that the product of the Higgs production
cross-section and the branching fraction BR(${H\rightarrow\thinspace ZZ^\ast}$)
can be measured with a relative statistical uncertainty of 20% (3.0%) at a
centre-of-mass energy of 350 GeV (3 TeV) using semileptonic final states,
assuming an integrated luminosity of 1 ab$^{-1}$ (5 ab$^{-1}$).
