A new device in operator calculus is introduced to treat expressions which contain non-commutable factors. By means of this technique the defining equation for the generator of transformation function of exponential type is derived. It is shown that this equation contains exclusively commutators of relevant quantities. Then, making use of this peculiarity to the exponential formula, a method is proposed for analyzing the structure of transformation function out of a given Hamiltonian of the system, and this is explained by some examples. This method consists of following procedures: First, decomposition of given Hamiltonian into parts of different character and abstraction of elementary matrices from it. Second, formation of commutators between these matrices and extension, if necessary, of the set of matrices enumerated at the beginning to include new ones which appear through operation of commutation. The matrix ring thus obtained constitutes the frame work of the transformation function. Through the course of this analysis one can find the ground why problems which are already solved exactly can be treated easily, and also can obtain some instructions how one should proceed in the solution of a given problem.