Breast cancer is one of the deadliest types of cancer, and it comes in a wide variety of forms, resulting in a wide variety of detection methods. Several deep learning techniques have been applied to decrease unnecessary biopsies and lessen the burden on radiologists. One of the most popular architectures for this task is the Convolutional Neural Networks (CNNs). This paper aims to explore the integration of convolutional neural networks (CNN) and wavelet transform (WT) to identify the optimal combination and architecture of these methods for efficient detection of breast cancer in ultrasound images. To accomplish this task, the wavelet convolutional neural network (WCNN) structures are proposed and trained for the mission of screening breast cancer abnormalities embedded in ultrasound type of images. Compared with other two popular networks, ResNet50 and MobileNetV2, it has been found that the proposed WCNN has produced a satisfactory solution, with an accuracy of 98.24%, precision of 97.29%, recall of 100%, and F measure of 98.24%.