The problem of pole assignment, by constant output feedback controllers, is studied for minimal systems described by a proper transfer function matrix G(s) is an element of R(mxp)(s) With McMillan degree n. A new method is presented based on asymptotic linearisation (around a degenerate point) of the pole placement map related to the problem. The essence of the present approach is to reduce the multilinear nature of the problem to one of solving a linear set of equations, and this is achieved without losing any of the degrees of freedom in the controller. The solution is given in closed form in terms of a one-parameter (epsilon) family of Static feedback compensators, for which the closed-loop poles approach the required ones as epsilon --> 0. Conditions for the generic, as well as exact, solvability of the arbitrary pole placement problem are given in terms of the numbers m, p, n and the rank of a new system invariant, the D-restricted Plucker matrix. It is shown that the method works generically when mp > n, which (along with the boundary case mp = n) is the best possible condition as far as the number of states of the open-loop system is concerned, for achieving arbitrary pole placement via constant output feedback.