The Non-symmetry and Anti-packing Model (NAM) is an effective pattern representation model. In this paper, a new NAM image representation method by using the nonoverlapping square subpatterns, which is called the square NAM (SNAM) representation, is proposed. The idea of the SNAM representation is described. The square subpattern has its own significant characteristics when it is compared with other subpatterns such as the triangle and the rectangle, etc. Unlike the general triangle subpattern which needs to record three vertices of the triangle and unlike the rectangle subpattern which needs to record the coordinates of its starting point, length and width, the square subpattern needs to record only its starting point and the side. Therefore, as far as a single record of the square subpattern is concerned, it can save storage space more effectively. The theoretical and experimental results presented in this paper prove the efficiency and the effectiveness of the proposed SNAM representation method for binary images.