Optical coherence tomography (OCT) scanning is useful in detecting various retinal diseases. However, there are not enough ophthalmologists who can diagnose retinal OCT images in much of the world. To provide OCT screening inexpensively and extensively, an automated diagnosis system is indispensable. Although many machine learning techniques have been presented for assisting ophthalmologists in diagnosing retinal OCT images, there is no technique that can diagnose independently without relying on an ophthalmologist, i.e., there is no technique that does not overlook any anomaly, including unlearned diseases. As long as there is a risk of overlooking a disease with a technique, ophthalmologists must double-check even those images that the technique classifies as normal. Here, we show that our deep-learning-based binary classifier (normal or abnormal) achieved a perfect classification on 108,308 two-dimensional retinal OCT images, i.e., true positive rate = 1.000000 and true negative rate = 1.000000; hence, the area under the ROC curve = 1.0000000. Although the test set included three types of diseases, two of these were not used for training. However, all test images were correctly classified. Furthermore, we demonstrated that our scheme was able to cope with differences in patient race. No conventional approach has achieved the above performances. Our work has a sufficient possibility of raising automated diagnosis techniques for retinal OCT images from "assistant for ophthalmologists" to "independent diagnosis system without ophthalmologists".