We present a study of the S = -1 meson-baryon interaction, employing a chiral SU(3) Lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. The parameters of the model have been fitted to a large set of experimental scattering data in different two-body channels, to threshold branching ratios, and to the precise SIDDHARTA value of the energy shift and width of kaonic hidrogen. In contrast to other groups, we have taken into consideration the K- p -> K+ Xi(-) , K-0 Xi(0) reaction data, since we found in a previous work to be especially sensitive to the NLO parameters of the chiral Lagrangian. In the present work we also include the Born terms, which usually have very little effect, and find them to be non-negligible in the K- p -> K Xi channels, correspondingly causing significant modifications to the NLO parameters. We furthermore show that the importance of the Born terms becomes more visible in the isospin projected amplitudes of the K- p -> K Xi reactions. The measurement of processes that filter single isospin components, like the K(L)(0)p -> K+ Xi(0) reaction that could be measured at the proposed secondary K-L(0) beam at Jlab, would put valuable constraints on the chiral models describing the meson-baryon interaction in the S = -1 sector. (C) 2016 Elsevier B.V. All rights reserved.