It is well known that the saccadic system presents multiple asymmetries. Notably, temporal (as opposed to nasal) saccades, centripetal (as opposed to centrifugal) saccades (i.e., the recentering bias) and saccades from the abducting eye (as opposed to the concomitant saccades from the adducting eye) exhibit higher peak velocities. However, these naso-temporal and centripetal-centrifugal asymmetries have always been studied separately. It is thus unknown which asymmetry prevails when there is a conflict between both asymmetries, i.e., in case of centripetal nasal saccades or centrifugal temporal saccades. This study involved binocular recordings of eye movements to examine both the naso-temporal and centripetal-centrifugal asymmetries so as to determine how they work together. Twenty-eight participants had to make saccades toward stimuli presented either centrally or in the periphery in binocular conditions. We found that temporal and abducting saccades always exhibit higher peak velocities than nasal and adducting saccades, irrespective of their centripetal or centrifugal nature. However, we showed that the velocity advantage for centripetal saccades is only found for temporal and not for nasal saccades. Such a result is of importance as it could provide new insights about the physiological origins of the asymmetries found in the saccadic system.