A new algorithm for connected component labeling is presented in this paper. This algorithm requires only one scan through an image for labeling connected components. Once this algorithm encounters a starting pixel of a component, it completely traces all the contour pixels and all internal pixels of that particular component. This algorithm recognizes components one at a time in the image while scanning in raster order. This property will be very useful in areas such as image matching, image registration and content-based information retrieval etc. This algorithm is also capable of extracting contour pixels of an image and storing them in the order of clock-wise direction which will provide very useful information in many applications. Also this algorithm assigns consecutive label numbers for different components and hence needs a minimum number of labels. As our main research is on mammography image analysis for diagnosing breast cancers, we applied this algorithm to mammograms and measured performance of the algorithm in terms of processing time. This will be a useful algorithm in medical image analysis as a preprocessing tool.