  The crystal structure of Cs$_2$CuBr$_4$ is the same as that of
Cs$_2$CuCl$_4$, which has been characterized as a spin-1/2
quasi-two-dimensional frustrated system. The magnetic properties of
Cs$_2$CuBr$_4$ were investigated by magnetization and specific heat
measurements. The phase transition at zero magnetic field was detected at
$T_{\rm N}=1.4$ K. It was observed that the magnetization curve has a plateau
at about one-third of the saturation magnetization for magnetic field $H$
parallel to the $b$- and $c$-axes, while no plateau was observed for
$H\parallel a$. The field-induced phase transition to the plateau state appears
to be of the first order. The mechanism leading to the magnetization plateau is
discussed.
