This paper focuses on the issue of speckle noise and its suppression. Firstly, the multiplicative speckle noise model and its mathematical formulation are introduced. Then, certain de-noising methods are described together with possible improvements. On their basis, an improvement of Kuan method (KuanS) is proposed. Performance of proposed KuanS method is tested on real ultrasound images and synthetic images corrupted with speckle noise. PSNR, edge preservation, standard deviation of homogenous regions and SIR are used for the evaluation of quality of noise suppression. Performance of the KuanS is compared with other methods. The KuanS method achieves satisfactory results even in comparison with more complex methods (SRAD, wavelet based noise suppression).