Abstract: Let τ=(T,F) be a hereditary torsion theory, the concept of dual τ-Rickart module is introduced. A module M is called dual τ-Rickart if π^－1_τ(Im ψ－ ) =Im ψ+τ(M) is a direct summand of M for every ψ∈End(M).Properties of dual τ-Rickart module are studied, some equivalent characterizations to be dual τ-Rickart are given. Moreover, it is proved that M isτ-Rickart and M/(τ(M)) has C₂ condition if and only if M is dual τ-Rickart and M/(τ(M)) has D₂ condition.

Key words: dual τ-Rickart module, τ-Rickart module, direct summand