  We present the first model-independent measurement of the CKM unitarity
triangle angle $\phi_3$ using $B^{\pm}\to D(K_{\rm S}^0\pi^+\pi^-\pi^0)K^{\pm}$
decays, where $D$ indicates either a $D^{0}$ or $\overline{D}^{0}$ meson.
Measurements of the strong-phase difference of the $D \to K_{\rm
S}^0\pi^+\pi^-\pi^0$ amplitude obtained from CLEO-c data are used as input.
This analysis is based on the full Belle data set of $772\times 10^{6}$
$B\overline{B}$ events collected at the $\Upsilon(4S)$ resonance. We obtain
$\phi_3 = (5.7~^{+10.2}_{-8.8} \pm 3.5 \pm 5.7)^{\circ}$ and the suppressed
amplitude ratio $r_{B} = 0.323 \pm 0.147 \pm 0.023 \pm 0.051$. Here the first
uncertainty is statistical, the second is the experimental systematic, and the
third is due to the precision of the strong-phase parameters measured from
CLEO-c data. The 95% confidence interval on $\phi_3$ is
$(-29.7,~109.5)^{\circ}$, which is consistent with the current world average.
