The prototypical network (ProtoNet) is a few-shot learning framework that performs metric learning and classification using the distance to prototype representations of each class. It has attracted a great deal of attention recently since it is simple to implement, highly extensible, and performs well in experiments. However, it only takes into account the mean of the support vectors as prototypes and thus it performs poorly when the support set has high variance. In this paper, we propose to combine ProtoNet with local Fisher discriminant analysis to reduce the local within-class covariance and increase the local between-class covariance of the support set. We show the usefulness of the proposed method by theoretically providing an expected risk bound and empirically demonstrating its superior classification accuracy on miniImageNet and tieredImageNet.