In this paper a new result in the problem of pole assignment by gain output feedback is given. Roughly speaking, this result says that arbitrary pole assignment is possible for almost all systems ifn < r + m + nu - 1, r > mu, m geq nu. Heren, randmare the number of states, of inputs and of outputs, respectively, and ν and μ are the so-called controllability index and the observability index of the system, respectively. This result extends the author's previous one in . The basic idea in  is developed further and its geometrical meaning is amplified. The proof of the theorem itself gives a method of constructing a desired gain matrix. An example is given to show the feasibility of the algorithm.