  We present a systematic method of creating type-III Dirac cones from
degenerate directionally flat bands. Here, the directionally flat band means a
completely dispersionless band only in a certain direction. The key strategy is
to retain one of the directionally flat bands while making the other
dispersive, by adding a perturbation having a selected form of a Hamiltonian
matrix. Such a form of a perturbation is found by using the "molecular-orbital
representation" which we have developed to describe flat-band models. The
models thus obtained host type-III Dirac cones even without fine-tuning hopping
parameters. To demonstrate the ubiquity of this method, we study concrete
examples of two-band models and a four-band model.
