  In this paper, we present a generalization of the parameterization method,
introduced by Cabr\'{e}, Fontich and De la Llave, to center manifolds
associated to non-hyperbolic fixed points of discrete dynamical systems. As a
byproduct, we find a new proof for the existence and regularity of center
manifolds. However, in contrast to the classical center manifold theorem, our
parameterization method will simultaneously obtain the center manifold and its
conjugate center dynamical system. Furthermore, we will provide bounds on the
error between approximations of the center manifold and the actual center
manifold, as well as bounds for the error in the conjugate dynamical system.
