The National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR) data and meso-scale numerical simulation data are analyzed to reveal a mechanism for the formation of heavy rainfall in Northern China; this mechanism is the non-uniformly saturated instability induced by a dry intrusion. The dry intrusion and the accompanying downward transport of air with a high value of potential vorticity (PV) are maintained during the precipitation event. As the dry air intrudes down into the warm and moist sector in the lower troposphere, the cold, dry air and the warm, moist air mix with each other, and, as a result, the atmosphere becomes non-uniformly saturated. On the basis of this non-uniform saturation, a new Brunt-Vaisala frequency (BVF) formula is derived and applied to the precipitation event. It is shown that, compared to the conditions of either a dry or a saturated atmosphere, the BVF in a non-uniformly saturated, moist atmosphere (BVF*) may be more appropriate for depicting the atmospheric instability in rainy regions.