We report the discovery of a possible planet in microlensing event MOA-2010-BLG-353. This event was only recognized as having a planetary signal after the microlensing event had finished, and following a systematic analysis of all archival data for binary lens microlensing events collected to date. Data for event MOA-2010-BLG-353 were only recorded by the high-cadence observations of the OGLE and MOA survey groups. If we make the assumptions that the probability of the lens star hosting a planet of the measured mass ratio is independent of the lens star mass or distance, and that the source star is in the Galactic bulge, a probability density analysis indicates the planetary system comprises a 0.9(-0.53)(+1.6) M-Saturn mass planet orbiting a 0.18(-0.11)(+0.32) M-circle dot red dwarf star, 6.43(-1.15)(+1.09) kpc away. The projected separation of the planet from the host star is 1.72(-0.48)(+0.56) au. Under the additional assumption that the source is on the far side of the Galactic bulge, the probability density analysis favours a lens system comprising a slightly lighter planet.