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From a very extensive set of radial velocities obtained at Fairborn Observatory we have computed a new spectroscopic orbit for HR 672. This binary has an orbital period of 93.290 days and an eccentricity of 0.5249. The greatly improved orbital elements have been incorporated into a new astrometric orbit, which has an inclination of 110°, from Hipparcos data. The primary is a slowly rotating early G star that is situated nearly 1 mag above the main sequence and is likely pseudosynchronously rotating. It has an iron abundance that is greater than that of the Sun. Lines of the secondary were not detected at red wavelengths, consistent with an adopted M0 dwarf spectral type. The age of the system is estimated to be about 5 billion years. The binary is a good candidate for interferometric resolution at infrared wavelengths.