Detecting breast lesions using ultrasound imaging is an important application of computer-aided diagnosis systems. Several automatic methods have been proposed for breast lesion detection and segmentation; however, due to the ultrasound artefacts, and to the complexity of lesion shapes and locations, lesion or tumor segmentation from ultrasound breast images is still an open problem. In this paper, we propose using a lesion detection stage prior to the segmentation stage in order to improve the accuracy of the segmentation. We used a breast ultrasound imaging dataset which contained 163 images of the breast with either benign lesions or malignant tumors. First, we used a U-Net to detect the lesions and then used another U-Net to segment the detected region. We could show when the lesion is precisely detected, the segmentation performance substantially improves; however, if the detection stage is not precise enough, the segmentation stage also fails. Therefore, we developed a test-time augmentation technique to assess the detection stage performance. By using the proposed two-stage approach, we could improve the average Dice score by 1.8% overall. The improvement was substantially more for images wherein the original Dice score was less than 70%, where average Dice score was improved by 14.5%. The proposed two-stage technique shows promising results for segmentation of breast US images and has a much smaller chance of failure.