We develop a new method to measure source proper motions in microlensing events , which can partially overcome problems due to blending . It takes advantage of the fact that the source position is known precisely from the microlensing event itself . We apply this method to the event MOA-2011-BLG-262 , which has a short timescale t _ { E } = 3.8 day , a companion mass ratio q = 4.7 \times 10 ^ { -3 } and a very high or high lens-source relative proper motion \mu _ { rel } = 20 { mas\ > yr ^ { -1 } } or 12 { mas\ > yr ^ { -1 } } ( for two possible models ) . These three characteristics imply that the lens could be a brown dwarf or a massive planet with a roughly Earth-mass “ moon ” . The probability of such an interpretation would be greatly increased if it could be shown that the high lens-source relative proper motion was primarily due to the lens rather than the source . Based on the long-term monitoring data of the Galactic bulge from the Optical Gravitational Lensing Experiment ( OGLE ) , we measure the source proper motion that is small , { \mbox { \boldmath$ \mu$ } } _ { s } = ( -2.3 , -0.9 ) \pm ( 2.8 , 2.6 ) { mas\ > yr ^ { -1 } } in a ( North , East ) Galactic coordinate frame . These values are then important input into a Bayesian analysis of the event presented in a companion paper by Bennett et al .