Cervical cancer screening, which involves classifying the abnormal types of cervical cells, can substantially reduce the morbidity and mortality of this widespread condition affecting women globally. Existing screening algorithms, however, lack trustworthiness, as they fail to indicate misclassified cells, which hinders their practical application. In this paper, we introduce a new and effective misclassification detection (MisD) algorithm that fully utilizes training data and a concise counterexamples (CEs) learning scheme, improving the trustworthiness of the classifier and further advancing its practical application. The key idea involves synthesizing CEs from training data through a linear combination of two randomly sampled training images, which are then utilized to train a mediator responsible for automatically auditing the misclassified cells. We evaluate this new MisD algorithm on two publicly available datasets (the largest two known to us), and the experimental findings verify its effectiveness, outperforming existing algorithms and, indeed, improving the trustworthiness of the classifier.