  We study a hermitian $(n+1)$-matrix model with plaquette interaction,
$\sum_{i=1}^n MA_iMA_i$. By means of a conformal transformation we rewrite the
model as an $O(n)$ model on a random lattice with a non polynomial potential.
This allows us to solve the model exactly. We investigate the critical
properties of the plaquette model and find that for $n\in]-2,2]$ the model
belongs to the same universality class as the $O(n)$ model on a random lattice.
