In this note, we present an improved algorithm to Schwartz, Sharir and Siegel's algorithm [8] for labeling the connected components of a binary image. Our algorithm uses the same bracket marking mechanism as is used in the original algorithm to associate equivalent groups. The main improvement of our algorithm is that it reduces the three scans on each line required by the original algorithm in its first pass into only one scan by using a recursive group-boundary dynamic tracking technique, while maintaining the computation on each pixel during scan still a constant time. This algorithm is fast enough to handle images in real time and simple enough to allow an easy and very economical hardware implementation.