In this note, we argue that the axiomatic requirement of range to the measure of aggregated total uncertainty (ATU) in Dempster-Shafer theory is not reasonable. Keywords: Dempster-Shafer theory, Uncertainty measure Dempster-Shafer theory [1, 2] is widely applied to uncertainty modeling [3, 4]. Two types of uncertainty, namely nonspecificity and discord, are coexisting in the Dempster-Shafer theory [5, 6]. A justifiable measure to these uncertainty is necessary to describe the essential characters of basic probability assignment function(BPA). To be justifiable, for a measure called as aggregated total uncertainty (ATU), some requirements are necessary.