The decuplet baryons, Delta. Sigma*, Xi*, and Omega(-), 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 Delta baryon are more affected by the medium against the Omega-state, containing three strange quarks, whose mass and residue are not considerably affected by the medium. We also find the vector and scalar self-energies of these baryons in nuclear matter. By the recent progresses at the PANDA experiment at the FAIR and NICA facility, it may be possible to study the in-medium properties of such states, even the multistrange. Xi* and Omega-systems, in the near future.