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Repeated measurements of eleven FK5 stars were performed with the north-south and east-south astrometric baselines of the Mark III optical interferometer in order to estimate the accuracy of wide-angle astrometry. Even though the declination range of these stars is insufficient to determine absolute declinations, we were able to determine corrections to the FK5 positions at four epochs with an accuracy of about 13 mas in declination and 23 mas in right ascension. Measurements at two different wavelengths were used to correct for refractive index fluctuations in a turbulent atmosphere. The pathlength difference between the two arms of the interferometer was monitored during the night with an internal white-light interferometer. The accuracy of the positions is limited by systematic errors due to unmonitored changes in the baseline coordinates and low-frequency water vapor fluctations. However, these results demonstrate the potential of future optical interferometers for the measurement of stellar positions with mas accuracy.