We have observed a clear peak below the Sigma(+)-production threshold in the He-4(K-, pi(-)) reaction at 600 MeV/c and theta(K pi) = 4 degrees. This is confirmation of the existence of the bound state of He-4(Sigma), which was reported in the He-4(stopped K-, pi(-)) reaction. As in the case of stopped kaons, no such peak was found in the He-4(K-, pi(+)) spectrum. Quantitatively reliable parameters for this level have been established. The binding energy and the width of the bound state are 4.4 +/- 0.3(stat) +/- 1(syst) MeV and 7.0 +/- 0.7(stat)(-0.0)(+1.2)(syst) MeV, respectively.