Six highly excited 1pig states of the Na2 molecule have been investigated by optical-optical double resonance (OODR) flourescence excitation spectroscopy. Absolute vibrational numberings are determined and molecular constants and RKR potential curves are obtained. The lowest 10 1pig states have been relabeled according to the hydrogenic nllambda characters of the Rydberg orbital and classified into core-penetrating and core-nonpenetrating Rydberg states.