Abstract: If a parcel of air is displaced slightly upward in an unsatured atmosphere, it will cool by adiabatic expansion. If the atmosphere is saturated, upward displacements are also accompanied by condensation and latent heating. After an infinitesimal perturbation, the condensed liquid water will drop partially out of the parcel. This phenomenon was not described in the Brunt-V3/4is3/4l3/4 frequency(Nm2) in previous studies, although they have been studied in many aspects, especially in the stability reduction quantified by deriving an expression for the saturat ed Brunt-V3/4is3/4l3/4 frequency(Nm2). At the same time, deriving an expression for equivalent potential temperature(θe) in previous studies also omits a term, mixing ratio of saturated vapor in air parcel. For simplicity, we consider only liquid-vapor phase transitions during derivation. A new formula of expressing Nm2, according to an air parcel change in a saturated at mosphere, is derived, discussed, and compared with original expression. It contains an additional term: the liquid water dropping partially out of the parcel, so that the new formula of expressing Nm2 accurately describes an air parcel change in a saturated atmosphere, it is useful in theory. In Section 3, an accurate formula of expressing θe is derived under the condition that no neglecting the mixing ratio of saturated vapor. Results are estimated and compared with two other θe formulas. Results of the new equivalent potential temperature (θe) are showed the less error in middle and high at mosphere. These two revised formulas Nm2 and θe describing the stability of a saturated atmosphere are reasonably accurate and applicable for the dynamic diagnosis.