Negative selection algorithms play an important role in anomaly detection. Interface detectors are a special negative selection algorithm that completely eliminates outer holes, but there are detection blind areas. In this paper, a novel negative selection algorithm with a hypercube interface detector is proposed. It uses self-sample clusters to construct self space, and boundary self-sample clusters to describe the interface detector. It eliminates the detection blind area and improves the detection rate. To validate the performance of the proposed method, experiments were conducted using the iris dataset, the skin segmentation dataset, and the Breast Cancer of Wisconsin (BCW) dataset. Experimental results show that the proposed method in this paper has a higher detection rate, lower false alarm rate, and fewer detectors than other anomaly detection methods for the same parameters.