This work examines the problem to describe an efficient algorithm for obtaining $n^2 \times n^2$ Sudoku matrices. For this purpose, we define the concepts of $n\times n$ $Π_n$-matrix and disjoint $Π_n$-matrices. The article, using the set-theoretical approach, describes an algorithm for obtaining $n^2$-tuples of $n\times n$ mutually disjoint $Π_n$ matrices. We show that in input $n^2$ mutually disjoint $Π_n$ matrices, it is not difficult to receive a Sudoku matrix.