We develop a generalized principle of electromagnetically induced transparency (EIT) vector magnetometry based on high-contrast EIT resonances and the symmetry of atom-light interaction in the linearly polarized bichromatic fields. Operation of such vector magnetometer on the D 1 line of 87 Rb has been demonstrated. The proposed compass-magnetometer has an increased immunity to shifts produced by quadratic Zeeman and ac-Stark effects, as well as by atom-buffer gas and atom-atom collisions. In our proof-of-principle experiment the detected angular sensitivity to magnetic field orientation is 10 −3 deg/Hz 1/2 , which is limited by laser intensity fluctuations, light polarization quality, and magnitude of the magnetic field.