There are numerous asymmetries in anatomy between the nasal and temporal hemiretinae, which have been connected to various asymmetries in behavioral performance. These include asymmetries in Vernier acuity, saccade selection, and attentional function, in addition to some evidence for latency differences for saccadic eye movements. There is also evidence for stronger retinotectal neural projection from the nasal than the temporal hemiretina. There is, accordingly, good reason to predict asymmetries in saccadic performance depending on which hemifield the saccade trigger stimuli are presented in, but the evidence on this is mixed. We tested for asymmetries in both saccade latency and landing point accuracy in a variety of different saccade tasks. We found no evidence for any asymmetries in saccade latency and only modest evidence for asymmetries in landing point accuracy. While this lack of asymmetry is surprising in light of previous findings of attentional asymmetries, it may reflect that cortical input to midbrain eye control centers mitigates any retinal and retinotectal asymmetry.