Decoherence is a fundamental obstacle to the implementation of large-scale and low-noise quantum information-processing devices. We suggest an approach for suppressing errors by employing preprocessing and postprocessing unitary operations, which precede and follow the action of a decoherence channel. In contrast to quantum error correction and measurement-based methods, the suggested approach relies on specifically designed unitary operators for a particular state without the need in ancillary qubits or postselection procedures. We consider the case of decoherence channels acting on a single qubit belonging to a many-qubit state. Preprocessing and postprocessing operators can be either individual, which is acting on the qubit effected by the decoherence channel only, or collective, which is acting on the whole multiqubit state. We give a classification of possible strategies for the protection scheme, analyze them, and derive expressions for the optimal unitary operators providing the maximal value of the fidelity regarding initial and final states. Specifically, we demonstrate the equivalence of the schemes where one of the unitary operations is individual while the other is collective. We then consider the realization of our approach for the basic decoherence models, which include single-qubit depolarizing, dephasing, and amplitude damping channels. We also demonstrate that the decoherence robustness of multiqubit states for these decoherence models is determined by the entropy of the reduced state of the qubit undergoing the decoherence channel.