Let R be a semilocal Dedekind domain, and let K be the field of fractions of R. Let G be a reductive semisimple simply connected R-group scheme such that every semisimple normal R-subgroup scheme of G contains a split R-torus G_{m , R}. It is proved that the kernel of the map(Formula Presanted.)induced by the inclusion of R into K is trivial. This result partially extends the Nisnevich theorem.