The 4(1)Sigma(+) state in KLi, characterized by a potential energy curve of irregular shape, is investigated experimentally. Spectra of the 4(1)Sigma(+) <- X-1 Sigma(+) band system, simplified by polarization labelling, are recorded and analyzed. The Inverted Perturbation Approach method is used to construct the exotic molecular potential of the 4(1)Sigma(+) state. The result is compared with the prediction of theoretical calculations. (c) 2010 Elsevier B. V. All rights reserved.