Breast ultrasound (BUS) images are commonly influenced by speckle noise as a result of the phenomenon. Most types of speckle noise are a multiplicative one. Speckle removing while preserving image's edges and image's contrast is a challenge. More researches have been done throw the literature trying to fix a development at this point. Here, a modest scheme based on combining wavelet denoising and intuitionistic fuzzy enhancement has been proposed. Also, double thresholding image segmentation followed by some morphological operations were applied after the proposed approach. The proposed approach has been applied with a sonogram image of a breast having a benign cancer. Performance evaluation of the work has been achieved utilizing four quantitative metrics: mean square of error (MSE), peak signal to noise ratio (PSNR), structural similarity index measure (SSIM), and the quantitative metric of edges' conservation: Pratt's figure of merit (FOM). Also, the method has been applied by a BUS image with a malignant cancer and a gray scale phantom. The final quantitative as well as qualitative results confirmed that the introduced approach could achieve an efficient success into breast cancer characterization through BUS images' investigation, helping in better clinical diagnosis and more explicit detection for breast cancers.