The damping rate of the poloidal flow in a tokamak is determined in the banana regime as an initial value problem. The bounce averaged drift kinetic equation is solved analytically for early times, and on longer time scales (of the order To) a numerical solution is performed. Initial conditions are chosen for the ion distribution function t = 0) describing states with similar flows ug(t = 0), but differing structure in the pitch angle variable A = 2/x/t;^. At early times an analytical treatment shows that the damping characteristics of ug{t) depend sensitively on whether the ions responsible for the flow be close to the trapped-passing boundary. Initial decay is shown to be of the form ^ ~ A numerical treatment then confirms this early time result and extends the solution to the long term aymptotic decay, which is found to be independent of the initial preparation of the system. A spread of characteristic times are estimated for differing initial conditions and in terms of the ion-ion collision frequency tu can be written Tp % 0.2 — O.Grf,-. The previous attempts at such a calculation are criticised and, as far as possible, explained in terms of the present work. The paper by Shaing and Hirshman (1989) claims an inverse aspect ratio dependence of Tp DC and this result is found to be most compatible with the asymptotic result of the present work.