Faint high-latitude carbon stars (FHLCs) are distant, luminous giants. For this reason, they are often used to study the dynamical and chemical properties of the Galactic Halo. However, a more accurate investigation of photometric and spectroscopic surveys has revealed an increasing number of such objects with luminosities of main sequence stars. We report the first results of a systematic search of FHLCs using the Digitized First Byurakan Survey (DFBS) low-resolution spectral database. The DFBS low-resolution spectral plates are analysed to find new faint early and late-type carbon star candidates. Twenty new faint high-latitude carbon star candidates have been detected in an area of ∼4030 sq. deg. Moderate-resolution slit spectroscopy was carried out for all candidates, confirming the carbon star nature for thirteen of them (nine are new discoveries), while the remaining objects are M-type stars. The carbon star sample consists of five N-type carbon stars, for which the estimated mass-loss rates agree well with the typical ones found for such carbon stars; five comparatively bright CH-type carbon stars; and three are probably dwarf carbon (dC) stars. The distance determination indicates that the dwarf carbon stars belong to the thin disk, while the other stars belong the Galactic halo. These results demonstrate that one can efficiently find new faint high-latitude carbon star in the Digitized First Byurakan Survey database.