High-resolution spectra of the (3)(II)-I-1 -> (2)(II)-I-1 system of the KRb molecule, obtained after excitation with fixed Ar+ laser frequencies, were recorded on a Connes-type Fourier transform interferometer. Our spectral observations led to the reassignment by 6 quanta of the vibrational numbering for the (2)'Pi state reported by Kasahara et al. [J. Chem. Phys. 111 (1999) 8857]. Molecular constants of the first 19 vibrational levels of the (2)(II)-I-1 state are determined by mixing the present work results and those of Kasahara et al. The potential energy curve is derived. The main spectroscopic constants for this highly perturbed electronic state of the (KRb)-K-39-Rb-85 isotopic species are: T-e = 15 902.06 (0.18) cm(-1); omega(e) = 49.76 (0.17) cm(-1); B-e = 0.02438 (5) cm(-1); R-e = 5.088 Angstrom; D-e = 1358.19 (0.80) cm(-1).