A variational calculation scheme is proposed to tackle the non-unitarity problem in the Dyson boson description of nuclear collective motion. It is based on a trial-state-optimization variational principle in which one minimizes the deviation of a trial state from being an exact eigenstate, instead of minimizing the energy expectation value in the trial state as is usually done in standard variational calculations. The viability of this variational method is demonstrated through an application to a monopole pairing interaction for multi-j shells.