We outline the construction of a refined version of the New Luyten Two-Tenths (NLTT) catalog of high proper motion stars, which will contain improved astrometry and photometry for the vast majority of the ~59,000 stars in NLTT. The bright end is constructed by matching NLTT stars to Hipparcos, Tycho-2, and Starnet; the faint end by matching to USNO-A and the Two Micron All Sky Survey (2MASS). In this first paper, we detail the bright-end matching procedure. We show that for the majority of stars in his catalog, Luyten measured positions accurate to 1" even though he recorded his results much more coarsely. However, there is a long tail of position errors, with one error as large as 11°. Proper-motion errors for the stars with small position errors are 24 mas yr-1 (1 σ) but deteriorate to 34 mas yr-1 for stars with inferior positions. NLTT is virtually 100% complete for V<~11.5 and |b|>15deg, but completeness in this magnitude range falls to ~75% at the Galactic plane. Incompleteness near the plane is not uniform, but is rather concentrated in the interval -80deg<l<20deg, where the Milky Way is brightest.