Non-conflicting and conflicting parts of belief functions are introduced in this study. The unique decomposition of a belief function defined on a two-element frame of discernment to non-conflicting and indecisive conflicting belief function is presented. Several basic statements about algebra of belief functions on a general finite frame of discernment are introduced and unique non-conflicting part of a BF on an $n$-element frame of discernment is presented here.
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