Abstract: The decomposition of linear time-invariant systems is discussed from the view point of the general complement space. It is pointed that by using the natural base as the base of the complement space, the inverse matrix of nonsingular transformation matrix can be obtained most easily. In general, the canonical decomposition can not be obtained by the intersection space method in the sense of the orthogornal complement space. Therefore, a different approach to the canonical decomposition is presented, which is concerned with the general complement space definition. It is proved that the basic-uncontrollable state variables, the basic-observable state variables and the basic-observable-uncontrollable State variables are invariant with respect to choices of the transformation matrix.