We propose a meta learning algorithm utilizing a linear transformer that carries out null-space projection of neural network outputs. The main idea is to construct a classification space such that the error signals during few-shot training are zero-forced on that space. The final decision on a test sample is obtained utilizing a null-space-projected distance measure between the network output and label-dependent weights that have been trained in the initial meta learning phase. Our meta learner achieves the best or near-best accuracies among known methods in few-shot image classification tasks with Omniglot and miniImageNet. In particular, our method shows stronger relative performance by significant margins as the classification task becomes more complicated.