The (0,1) band of the B-2 Sigma(u)(+)-X-2 Sigma(g)(+) system of N-14(2)+ and N-15(2)+ has been observed using the fast ion beam laser spectroscopy (FIBLAS) technique. In total, 80 rotational lines were identified as belonging to the (0,1) band. These laser-induced fluorescence (LIF) data for the B-X band, combined with the Fourier transform (FT) emission data for the Meinel A(2) Pi(u)-X-2 Sigma(g)(+) system, allow us to remove the strong correlation between the X and B states and thus properly determine uncorrelated values of the molecular constants for the excited B and perturbed A states. Also, the values of equilibrium molecular constants are reevaluated for N-14(2)+ and N-15(2)+.