A new method for extracting lines from discrete binary images is proposed. The algorithm is capable of extracting individual lines and producing a structure-descriptive representation for every line extracted. The algorithm could be considered as an extension of Wakayama's Maximal Square Moving (MSM) algorithm[37] since pseudo maximal squares are substituted for maximal squares, but essentially, it is distinct from the MSM algorithm because squares are derived only in the most desirable direction while tracking a line. The resulting representation of a line is a set of points that are the centers of the pseudo maximal squares along the tracked line. This information is highly conducive to creating a high-level mathematical representation of the line being tracked. Examples are given for regions of a complex map.