Let R be a Noetherian ring, M be an R-module and let d be a non-negative integer. the authors introduce the R-module Ud(M) and the functor Td(-) on the category of R-modules. General concerning results on the module Td(M) and its relationship with d-local cohomology modules Hd(M) will be given. Then, whenever M is finitely generated, under a mild condition the authors show that Td(M) ~ or = Ud(M), which turns out a result on the finiteness of the set AssR(Td(M)). Finally a criterion for the isomorphism M ~ or = Ud(M) will be given.