Most of tight-binding studies of transition metal based systems deviating from perfect bulk (surfaces, nanoparticles, alloys) are based on local charge neutrality rules per site, per valence orbital and per element. Unfortunately, such rules do not hold per spin when interested in magnetic elements. We present here a simple way to characterize the variation of the magnetic moment with the environment and to generalize the tight-binding expression of the energy to account for magnetism. This is illustrated in the particular case of cobalt, going from perfect pure bulk to surface, nanoparticles and then CoPt alloy. (C) 2015 Elsevier B.V. All rights reserved.