  We consider an operator $\Delta^2 + A(x)\cdot D+q(x)$ with the Navier
boundary conditions on a bounded domain in $R^n$, $n\ge 3$. We show that a
first order perturbation $A(x)\cdot D+q$ can be determined uniquely by
measuring the Dirichlet--to--Neumann map on possibly very small subsets of the
boundary of the domain. Notice that the corresponding result does not hold in
general for a first order perturbation of the Laplacian.
