We study the active 4-state Potts model (APM) on the square lattice in which active particleshave four internal states corresponding to the four directions of motion. A local alignment rule in-spired by the ferromagnetic 4-state Potts model and self-propulsion via biased diffusion according tothe internal particle states leads to flocking at high densities and low noise. We compute the phasediagram of the APM and explore the flocking dynamics in the region, in which the high-density(liquid) phase coexists with the low-density (gas) phase and forms a fluctuating band of coherentlymoving particles. As a function of the particle self-propulsion velocity, a novel reorientation transi-tion of the phase-separated profiles from transversal to longitudinal band motion is revealed, whichis absent in the Vicsek model and the active Ising model. We further construct a coarse-grainedhydrodynamic description of the model which validates the results for the microscopic model.