Abstract: Considering the latent heating effect, a new form of Q vector containing the generalized potential temperature was derived. Based on this new Q vector, the corresponding non-geostrophic Omega equation was further developed. (1) The newly-derived Q vector consists of the enstrophy stretched vector, frontogenesis vector and the gradient of latent heating, and its divergence was the only forcing term in the Omega equation. (2) With the new Q vector, a heavy rainfall event occurred in North China was studied. It is found that the divergence of the Q vector can represent the structure of the vertical motions within the precipitation area. It comprehensively reflects the secondary vertical circulations, the frontogenesis and frontolysis, the large-scale and meso-scale forcing, etc. These physical processes are all important factors to the occurrence and development of heavy rainfall, and therefore the new Q vector showed a close relationship to the heavy precipitation. (3) Using the 24 h forecasting data from the Global Forecasting System to calculate the Q vector, the results showed that the forecasting Q vector convergence has close relationship with observed 6 h precipitation. This means that a prediction could be made based on the newly-derived Q vector.