We report a new measurement of the photoionization cross section for the (2p)5(3p) 3D3 state of neon at the wavelengths of 351 and 364 nm. These data were obtained by monitoring the decay of the fluorescence of atoms trapped in a magneto-optical atom trap under the presence of a photoionizing laser, a technique developed by Dinneen et al. [Opt. Lett. 17, 1706 (1992)]. We obtain absolute photoionization cross sections of 2.05ᰮ25ױ0-18 cm2 at =351 nm and 2.15ᰮ25ױ0-18 cm2 at =364 nm, an improvement in accuracy of a factor of 4 over previously published values. These new values are not consistent with published theoretical data.