Herein we introduce a reliable and effective method, allowing any musician, regardless of the theoretical background, to carry out a 4-way jazz harmonization of whatever melodic progression almost instantly, with few exceptions. Many jazz students experience a deep frustration in dealing with the harmonization of non-diatonic notes. Sometimes, moreover, a coherent harmonization of the aforementioned notes can turn out to be a very challenging task even for extremely skilled professionals. In this paper, the harmonization of the chromatic scale in different harmonic contexts is accurately discussed, by resorting to the well-known concepts of harmonic functions, tonicization, chromatic and diatonic parallelism, and auxiliary chords. All the chords are labelled so as to allow the reader to immediately understand their role in the particular harmonic context. Consequently, the procedure essentially translates into an optimization of the "harmonic flow".