An approach to the read-out problem of the shift of surface plasmon resonance (SPR) dip and an experimental arrangement for its realization are considered. The principle of the proposed registration method is based on the measurement of the ratio of the p- and s-polarized components in reflected light, giving a sensitivity enhancement of up to two orders of magnitude. The described set-up can be employed to monitor biospecific interactions, producing refractive-index changes near the detection limit of the SPR technique using only p-polarized light.