The polarization of extracted SATURNE II proton beam as a function of different ion source configurations was studied. Two distinct experiments were necessary for this purpose. In the first one, the LEFT-RIGHT instrumental asymmetry of the beam polarimeter was determined using an unpolarized beam. In the second one this correction factor was applied to asymmetries measured with the beam from the polarized ion source in all polarization states. The measurements were carried out at the proton beam kinetic energy 0.80 GeV, where the pp-elastic scattering analyzing power is near its maximum. The results confirmed that the two so-called “unpolarized states” of the source were polarized to several percent, whereas the absolute values of the beam polarizations in the so-called “polarized states” were equal and opposite. It was observed that the hexapole lens of the ion source produced beam polarization in the absence of any transition. The beam polarization as a function of hexapole current, transition field attenuation, and spin rotation solenoid current was measured. It was also shown how to obtain a strictly unpolarized beam using the polarized source only. The results obtained with the SATURNE II ion source HYPERION may also be relevant to similar sources at other accelerators.