  Using exact diagonalizations of finite clusters with up to 32 sites, we study
the $J_1-J_2$ model on the 1/5 depleted square lattice. Spin-spin correlation
functions are consistent with plaquette order in the spin gap phase which
exists for intermediate values of $J_2/J_1$. Besides, we show that singlet
states will be present in the singlet-triplet gap if $J_2/J_1$ is not too small
($J_2/J_1 \gtrsim 0.47$). We argue that this property should play a central
role in determining the exchange integrals in ${\rm CaV}_4{\rm O}_9$
