Most of the existing biclustering algorithms take into account the properties that hold for a set of objects. However, it could be very useful in several application domains such as organized crime, genetics or digital marketing to identify homogeneous groups of similar objects in terms of both the presence and the absence of attributes. In this paper, we present a generic method of biclustering that exploits a binary matrix to produce at least three types of biclusters: (i) those where all values are equal to 1, (ii) those where all values are equal to 0, and (iii) those indicating the presence of certain attributes and/or the absence of other attributes without the need to take into account the complementary of the initial binary context (matrix). The implementation and validation of the method on data sets illustrate its potential in the discovery of relevant patterns.