Pattern substitution (PS) method (Ho et al., Comput. Stand. Interfaces 31:787-794, 2009) is a recent reversible data hiding method for binary images. It generates one pattern pair, the patterns in which are called PM and PF, and substitutes between them to embed one bit. Two types of PS have been proposed: non-overlapping PS and overlapping PS. However, Dong et al. (ETRI J. 37:990-1000(ETRI J. 37:990- , 2015 states that the overlapping PS sometimes cannot decode correctly, which is called as miscoding problem. Moreover, to the PS-based methods (Ho et al., Comput.