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(ProQuest: ... denotes formulae and/or non-USASCII text omitted)We present the discovery of a new dwarf galaxy, Perseus I/Andromeda XXXIII, found in the vicinity of Andromeda (M31) in stacked imaging data from the Pan-STARRS 1 3[pi] survey. Located 27.[degrees]9 away from M31, Perseus I has a heliocentric distance of 785 + or - 65 kpc, compatible with it being a satellite of M31 at ... kpc from its host. The properties of Perseus I are typical for a reasonably bright dwarf galaxy (M sub(v) = -10.3+ or -0.7), with an exponential half-light radius of r sub(h) = 1.7 + or - 0.4 arcmin or ... pc at this distance, and a moderate ellipticity (...). The late discovery of Perseus I is due to its fairly low surface brightness (... mag arcsec super(-2)), and to the previous lack of deep, high quality photometric data in this region. If confirmed to be a companion of M31, the location of Perseus I, far east from its host, could place interesting constraints on the bulk motion of the satellite system of M31.