We propose a new approach to minimize the instrumental polarization (IP) of current polarimetric observations. It is shown how the instrumental polarization can be deduced and removed, by using lines with no intrinsic linear polarization. Notably, no specific understanding of the polarizing properties of our optical setup is required. For the technique to be of practical application, lines unaffected by IP presenting various temperature, magnetic field, etc. sensitivities must be identified. We work out the atomic levels involved in electric dipole transitions which create no linear polarization, from the Zeeman effect.