In this paper we describe a fast procedure for re-training a feed-forward network, previously trained by error back-propagation, following a small change in the training data. This technique would permit fine calibration of individual neural network based control systems in a mass-production environment. We also derive a generalised error back-propagation algorithm which allows an exact evaluation of all of the terms in the Hessian matrix. The fast re-training procedure is illustrated using a simple example.