The center of our Galaxy is a known strong source of electron-positron 511 keV annihilation radiation. Thus far, however, there have been no reliable detection of annihilation radiation outside of the central radian of our Galaxy. One of the primary objectives of the INTEGRAL (International Gamma-Ray Astrophysics Laboratory mission, resolution, coded-apeture gamma-ray telescope with an unprecedented combination of sensitivity, angular resolution, and energy resolution. We resport results from the first 10 months of observation. During this period a significant fraction of the observing time was spent in or near the Galactic plan. No positive annihilation flux was detected outside of the central regin ( l \u3e 40°) of our Galaxy. In this paper we describe observation and data analysis method and give limits on the 511 keV flu