This paper presents a novel anisotropic diffusion (AD) filter for despeckling of ultrasound images using a non-linear conductance function. Proper choice of the conductance function while applying AD filters is extremely critical. This work proposes an improved conductance function that tends to suppress speckle with due preservation of diagnostic features. The diffusion coefficient of the AD filter thus decreases monotonically and acts as an edge seeking as well as preserving function. Peak Signal to Noise Ratio (PSNR), Coefficient of Correlation (CoC) and Speckle Suppression Index (SSI) are the quality metrics used for performance evaluation of the proposed despeckling filter.