Science and Education Publishing Journal of Mathematical Sciences and Applications 1 1 2013 10 09 On an Algorithm for Obtaining All Binary Matrices of Special Class Releted to V. E. Tarakanov’s Formula 36 38 EN Krasimir Yordzhev Faculty of Mathematics and Natural Sciences, South-West University “N. Rilsky”, Blagoevgrad, Bulgaria JMSA2013125 10.12691/jmsa-1-2-5 2013 09 23 2013 10 08 2013 10 09 An algorithm for obtaining all n×n binary matrices having exactly 2 units in every row and every column is described in the paper. After analysing the work of the algorithm a formula for calculating the number of these matrices has been obtained. This formula is known and has been obtained using other methods, which by their nature are purely analytical and not constructive. Thus a new, constructive proof of this known formula has been obtained.