We introduce a new wavelet-based method for edge detection in ultrasound (US) images. Each beam that is analyzed is first transformed into the wavelet domain using the continuous wavelet transform (CWT). Because the CWT preserves both scale and time information, it is possible to separate the signal into a number of scales. The edge is localized by first determining the scale at which the power spectrum, based on the wavelet transform, has its maximum value. Next, at this scale we find the position of the peak for the squared CWT. This method does not depend on any threshold, after the range of scales have been determined. We suggest a range of scales for US images in general. Sample edge detections are demonstrated in US images of straight and jagged edges of simple structures submerged in water bath, and of an abdominal aorta aneurysm phantom.