The query likelihood retrieval function has proven to be empirically effective for many retrieval tasks. From theoretical perspective, however, the justification of the standard query likelihood retrieval function requires an unrealistic assumption that ignores the generation of a "negative query" from a document. This suggests that it is a potentially non-optimal retrieval function. In this paper, we attempt to improve the query likelihood function by bringing back the negative query generation. We propose an effective approach to estimate the probabilities of negative query generation based on the principle of maximum entropy, and derive a more complete query likelihood retrieval function that also contains the negative query generation component. The proposed approach not only bridges the theoretical gap in the existing query likelihood retrieval function, but also improves retrieval effectiveness significantly with no additional computational cost.