  In this paper we study the inverse boundary value problem of determining the
potential in the Schr\"{o}dinger equation from the knowledge of the
Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in
the sense that, under general settings, the optimal stability estimate is of
logarithmic type. In this work, a Lipschitz type stability is established
assuming a priori that the potential is piecewise constant with a bounded known
number of unknown values.
