The measurement of solar magnetic fields using the Zeeman effect diagnostics has a fundamental 180° ambiguity in the determination of the azimuth angle of the transverse field component. There are several methods that are used in the community and each one has its merits and demerits. Here we present a disambiguation idea that is based on the assumption that most of the magnetic field on the sun is predominantly vertical. While the method is not applicable to penumbra or other features harboring predominantly horizontal fields like the sheared neutral lines, it is useful for regions where fields are predominantly vertical like network and plage areas. The method is tested with the full-disk solar vector magnetograms observed by the SOLIS/VSM instrument. We find that statistically about 60 - 85 % of the pixels in a typical full-disk magnetogram has a field inclination in the range of 0 - 30° with respect to the local solar normal, and thus can be successfully disambiguated by the proposed method. Due to its non-iterative nature, the present method is extremely fast and therefore can be used as a good initial guess for iterative schemes like the non-potential field computation (NPFC) method. Furthermore, the method is insensitive to noisy pixels as it does not depend upon the neighboring pixels or derivatives.