The authors construct certain lowest weight representations of the complex Lie superalgebra osp(4\(| 2)\) in terms of suitably chosen families of bosonic and fermionic creation and annihilation operators. These representations are unitary with respect to the star operation in osp(4\(| 2)\) corresponding to the real Lie subalgebra o(4)\(\times sp(2,{\mathbb{R}})\). Their decomposition on reduction to o(4)\(\times sp(2,{\mathbb{R}})\) is studied in detail.