Using V as the time-delay operator, a linear invariant time-delay system is expressed by a quadruple (A(δ)), B(δ) C(V) D(V)) with the matrices over a polynomial ring in V. This paper studies the decoupling and coefficient assignment of such a system. For a class of time-delay systems non-controllable over the polynomial ring in V but controllable over the field of rational functions in V, we present sufficient conditions under which the system characteristic polynomial may be determined arbitrarily by feasible control laws. Two examples are investigated to illustrate the theory.