In this paper, we propose a simple but effective specular highlight removal method using a single input image. Our method is based on a key observation - the maximum fraction of the diffuse color component (so called maximum diffuse chromaticity in the literature) in local patches in color images changes smoothly. Using this property, we can estimate the maximum diffuse chromaticity values of the specular pixels by directly applying low-pass filter to the maximum fraction of the color components of the original image, such that the maximum diffuse chromaticity values can be propagated from the diffuse pixels to the specular pixels. The diffuse color at each pixel can then be computed as a nonlinear function of the estimated maximum diffuse chromaticity. Our method can be directly extended for multi-color surfaces if edge-preserving filters (e.g., bilateral filter) are used such that the smoothing can be guided by the maximum diffuse chromaticity. But maximum diffuse chromaticity is to be estimated. We thus present an approximation and demonstrate its effectiveness. Recent development in fast bilateral filtering techniques enables our method to run over 200× faster than the state-of-the-art on a standard CPU and differentiates our method from previous work.