Both in theory and in many practical issues, a crucial role is played by the problem of solving systems of ordinary differential equations. One of these problems is the decomposition of the system of equations in blocks, i.e. in such a subsystem, each of which comprises a minimal number of unknown functions, both incoming and under the sign of the derivative and the right sides. Therefore, natural formulation of the problem of finding ways to convert these systems to splitting mind. For systems of linear equations, this problem is solved quite simply. This is tantamount to bringing the system matrix to Jordan form. Each cell corresponds to a Jordan block split system.