We have developed a new type of stimulated Raman adiabatic passage (STIRAP) that is applicable to a degenerated reaction system. The direction of the photon polarization vector is the adiabatic parameter in the STIRAP. The molecular handedness of H2POSH, a preoriented phosphinotioic acid that has two stable configurations, L and R enantiomers, is used as a model system. The control of molecular handedness in both pure and mixed state cases are considered. In the case of a pure state, a STIRAP with a linearly polarized single laser allows an almost complete transfer from an L (R) enantiomer to the other by adiabatically changing its polarization direction. The adiabatic criterion for changing the polarization direction is clarified. In the case of a mixed state, a STIRAP with two linearly polarized laser pulses allows a selective preparation of pure enantiomers from its racemic mixture. In the low temperature limit, a five-level model reduces a three-level model by setting the direction of the polarization of the pump and Stokes pulses in such a way that only the forward transfer is allowed, while the reverse is forbidden. Furthermore, in the case of mixed state, relaxation effects originating from vibrational mode couplings are taken into account, and the influence of the population decay from intermediate states on the STIRAP is compared with that by a pi-pulse approach.