Video anomaly detection is a challenging task because most anomalies are scarce and non-deterministic. Many approaches investigate the reconstruction difference between normal and abnormal patterns, but neglect that anomalies do not necessarily correspond to large reconstruction errors. To address this issue, we design a Convolutional LSTM Auto-Encoder prediction framework with enhanced spatio-temporal memory exchange using bi-directionalilty and a higher-order mechanism. The bi-directional structure promotes learning the temporal regularity through forward and backward predictions. The unique higher-order mechanism further strengthens spatial information interaction between the encoder and the decoder. Considering the limited receptive fields in Convolutional LSTMs, we also introduce an attention module to highlight informative features for prediction. Anomalies are eventually identified by comparing the frames with their corresponding predictions. Evaluations on three popular benchmarks show that our framework outperforms most existing prediction-based anomaly detection methods.