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For a regular uncountable cardinal κ and a cardinal λ with cf(λ) < κ < λ, we investigate the consistency strength of the existence of a stationary set in ${}_{\kappa }\lambda$ which cannot be split into λ⁺ many pairwise disjoint stationary subsets. To do this, we introduce a new notion for ideals, which is a variation of normality of ideals. We also prove that there is a stationary set S in ${}_{\kappa }\lambda$ such that every stationary subset of S can be split into λ⁺ many pairwise disjoint stationary subsets.