The Ramsey fringe contrast of a pulsed optically pumped cold atom clock is strongly affected by the transverse decay of the atomic sample. This letter calculates the Ramsey fringe with focus on transverse decay, and analyzes the Ramsey fringe contrast with different transverse decay rates. By fitting the experimental data, we obtain the transverse decay rate in a cold atom sample at an approximate value of 30.5 s-1, which is much smaller than that in a cell.