Connected components of edge pixels are valuable for many applications, e.g., Image segmentation, contour extraction, and text detection. However, a connected component of edge pixels may not form a simple curve due to the existence of bifurcation pixels, and thus limits its application in shape modeling. In this paper, we propose an approach to remove bifurcation pixels in an edge image, which let us remove bifurcation pixels in every connected component of edge pixels in an edge image. We present a case study of license plate detection to demonstrate an application of the proposed approach.