The construction of binary matrices has attained significance due to its potential for hardware-friendly implementation and appealing applications in compressed sensing (CS). A class of binary matrices with low coherence and flexible row sizes can be constructed from Euler Squares (ES). In this paper, we introduce a generalization of the ES concept, namely, Generalized Euler Square (GES). We show that the binary matrices designed from GES provide significant improvements in column size compared to the ones constructed from Euler square. Exploiting the properties of GES, we obtain that such constructed binary matrices possess block orthogonal structure. As a result, such binary matrices are suitable for the recovery of block sparse signals. © 1994-2012 IEEE.