The decuplet baryons, Δ, Σ^*, Ξ^* and Ω^-, are studied in nuclear matter by using the in-medium QCD sum rules. By fixing the three momentum of the particles under consideration at the rest frame of the medium, the negative energy contributions are removed. It is obtained that the parameters of the Δ baryon are more affected by the medium against the Ω^- state, containing three strange quarks, whose mass and residue do not affected by the medium, considerably. We also find the vector and scalar

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... elf energies of these baryons in nuclear matter. By the recent progresses at P̅ANDA experiment at FAIR and NICA facility it may be possible to study the in-medium properties of such states even the multi-strange Ξ^* and Ω^- systems in near future.