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We report on VLBI observations of M81*, the northwest-southeast orientednuclear core-jet source of the spiral galaxy M81, at five different frequenciesbetween 1.7 and 14.8 GHz. By phase referencing to supernova 1993J we canaccurately locate the emission region of M81* in the galaxy's reference frame.Although the emission region's size decreases with increasing frequency whilethe brightness peak moves to the southwest, the emission region seems sharplybounded to the southwest at all frequencies. We argue that the core must belocated between the brightness peak at our highest frequency (14.8 GHz) and thesharp bound to the southwest. This narrowly constrains the location of thecore, or the purported black hole in the center of the galaxy, to be within aregion of +/-0.2 mas or +/-800 AU (at a distance of ~4 Mpc). This rangeincludes the core position that we determined earlier by finding the moststationary point in the brightness distribution of M81* at only a singlefrequency. This independent constraint therefore strongly confirms our earliercore position. Our observations also confirm that M81* is a core-jet source,with a one-sided jet that extends to the northeast from the core, on averagecurved somewhat to the east, with a radio spectrum that is flat or invertednear the core and steep at the distant end. The brightness peak isunambiguously identified with the variable jet rather than the core, whichindicates limitations in determining the proper motion of nearby galaxies andin refining the extragalactic reference frame.Comment: LaTeX, 10 pages with 3 figures. Typos fixed and slight rewording for  clarity from previous version. Accepted for publication in the Astrophysical  Journa

The Location of the Core in M81