  We investigate the $K$-band luminosity distribution of galaxies in the region
of clusters at $z\sim1.2$ near to the radio galaxy 3C 324. The imaging data
were obtained during the commissioning period of the Subaru telescope. There is
a significant excess of the surface number density of the galaxies with $K =$
17--20 mag in the region within $\sim$ 40'' from 3C 324. At this bright end,
the measured luminosity distribution shows a drop, which can be represented by
the exponential cut off of the Schechter-function formula; the best-fitted
value of the characteristic magnitude, $K^{*}$, is $\sim 18.4\pm0.8$. This
measurement follows the evolutionary trend of the $K^*$ of the rich clusters
observed at an intermediate redshift, which is consistent with passive
evolution models with a formation redshift $z_f \gtsim 2$. At $K \gtsim 20$
mag, however, the excess of the galaxy surface density in the region of the
clusters decreases abruptly, which may imply that the luminosity function of
the cluster galaxies has a negative slope at the faint end. This may imply
strong luminosity segregation between the inner and outer parts of the
clusters, or some deficit of faint galaxies in the cluster central region of
the cluster.
