Decomposition of matrices with relational data, i.e. decomposition of Boolean matrices in our case, where the input matrix is represented as a product of two other Boolean matrices, is widely used in data mining. There exist several kinds of these matrix decompositions, and a lot of them are designed for real valued data. On the other hand, such methods are not tailored for Boolean data. The purpose of this thesis is to study matrix decomposition methods that are directly designed for Boolean data. In this thesis, we present a mathematical background and various methods---including our own methods---for Boolean matrix decomposition. We also present some experimental results obtained from these methods, performed on real and synthetic datasets. We also present some experimental results obtained from these methods, performed on real and synthetic datasets.