In the present paper it is shown that the fundamental zero-normalized solution of a system of linear homogeneous differential equations can be represented as a formal series of products of exponential matrices. If the system satisfies the conditions of the Perron theorem on the triangulation of a system of equations, then the solution of such a system can be represented as a finite product of exponential matrices. In addition, a formula for differentiating an exponential matrix function is derived, and the problem of constructing a transformation that reduces a system of homogeneous differential equations to a triangular form is considered.