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Breast cancer is a gigantic burden on humanity, causing the loss of enormous numbers of lives and amounts of money. It is the world's leading type of cancer among women and a leading cause of mortality and morbidity. The histopathological examination of breast tissue biopsies is the gold standard for diagnosis. In this paper, a computer-aided diagnosis (CAD) system based on deep learning is developed to ease the pathologist's mission. For this target, five pre-trained convolutional neural network (CNN) models are analyzed and tested—Xception, DenseNet201, InceptionResNetV2, VGG19, and ResNet152—with the help of data augmentation techniques, and a new approach is introduced for transfer learning. These models are trained and tested with histopathological images obtained from the BreakHis dataset. Multiple experiments are performed to analyze the performance of these models through carrying out magnification-dependent and magnification-independent binary and eight-class classifications. The Xception model has shown promising performance through achieving the highest classification accuracies for all the experiments. It has achieved a range of classification accuracies from 93.32% to 98.99% for magnification-independent experiments and from 90.22% to 100% for magnification-dependent experiments. [ABSTRACT FROM AUTHOR]