The proposed method of atmospheric total optical depth (TOD) determination is based on the assumption that TOD is an arbitrary smooth function of time. Any small section of this function can be approximated by a linear relationship. A redundant system of Bouguer equations corresponding to n solar observations (where n > 3) can be written for each linear section. This procedure is successively applied to each section of the TOD curve and yields (N - n + 1) systems of Bouguer equations, where N is the total number of solar observations during a day. Solving these systems of Bouguer equations gives an extra-atmospheric value of the solar flux and TOD curve parameters. The accuracy of the method depends on the accuracy of TOD curve approximation, i.e., on the character of TOD variation with time and a total number of observations during a day. The new method (named approximation by linear sections (APLS)) has been used for TOD investigations in the Crimea (a peninsula in Ukraine) since 1996. In comparison with the classical Bouguer-Langley method the new method allows us to achieve higher accuracy, when the conditions of astroclimate at the observational site are not very good and especially when the observations are carried out for a half day, i.e., only before noon or after.