  We measured the temperature dependence of the magnetic susceptibility and
specific heat and the magnetic-field dependence of the magnetization of
CuInVO$_5$. An antiferromagnetically ordered state appears below $T_{\rm N} =
2.7$ K. We observed a $\frac{1}{2}$ quantum magnetization plateau above 30 T at
1.3 K. We show that the spin system consists of antiferromagnetic
spin-$\frac{1}{2}$ tetramers with $J_1 = 240 \pm 20$ and $J_2 = -142 \pm 10$ K
for the intratetramer interactions.
