We present a novel and computationally efficient method for repairing a feed-forward neural network with respect to a finite set of inputs that are misclassified. The method assumes no access to the training set. We present a formal characterisation for repairing the neural network and study its resulting properties in terms of soundness and minimality. We introduce a gradient-based algorithm that performs localised modifications to the network's weights such that misclassifications are repaired while marginally affecting network accuracy on correctly classified inputs. We introduce an implementation, I-REPAIR, and show it is able to repair neural networks while reducing accuracy drops by up to 90% when compared to other state-of-the-art approaches for repair.