In this work, we propose CBiGAN -- a novel method for anomaly detection in images, where a consistency constraint is introduced as a regularization term in both the encoder and decoder of a BiGAN. Our model exhibits fairly good modeling power and reconstruction consistency capability. We evaluate the proposed method on MVTec AD -- a real-world benchmark for unsupervised anomaly detection on high-resolution images -- and compare against standard baselines and state-of-the-art approaches. Experiments show that the proposed method improves the performance of BiGAN formulations by a large margin and performs comparably to expensive state-of-the-art iterative methods while reducing the computational cost. We also observe that our model is particularly effective in texture-type anomaly detection, as it sets a new state of the art in this category. Our code is available at https://github.com/fabiocarrara/cbigan-ad/.