A rigorous and exact solution is obtained for the problem of the radiation of sound from a semi-infinite unflanged rigid duct with an internal acoustically absorbent lining. The solution is obtained by a modification of the normal Wiener-Hopf technique. The solution is in terms of an infinite series of unknowns, which are determined from an infinite set of simultaneous equations. The infinite system converges rapidly enough to make the solution suitable for numerical computations. Some numerical results are given in graphical form for the propagation of the principal symmetric mode in the duct.