We report the first experimental observation of the 3(1)Pi(u) state in the Na-2 molecule. Polarisation labelling spectroscopy technique is applied to deter-mine energies of about 500 levels in this state. We deduce a set of Dunham coefficients fitting levels with v less than or equal to 21. The spectroscopic data are used to construct a Rydberg-Klein-Rees potential for the state. Its main molecular constants, T-e, omega(e), and B-e, are found to be 31697.61(2), 103.169(7) and 0.105698(12) cm(-1), respectively. (C) 2004 Elsevier B.V. All rights reserved.