In trajectory-based operations, trajectory negotiation and verification are conducive to using airspace resources fairly, reducing flight delay, and ensuring flight safety. However, most of the current methods are based on route negotiation, making it difficult to accommodate airspace user-initiated trajectory requests and dynamic flight environments. Therefore, this paper develops a framework for trajectory negotiation and verification and describes the trajectory prediction, negotiation, and verification processes based on a four-dimensional trajectory. Secondly, users predict flight trajectories based on aircraft performance and flight plans and submit them as requested flight trajectories to the air traffic management (ATM) system for negotiation in the airspace. Then, a spatiotemporal weighted pattern mining algorithm is proposed, which accurately identifies flight combinations that violate the minimum flight separation constraint from four-dimensional flight trajectories proposed by users, as well as flight combinations with close flight intervals and long flight delays in the airspace. Finally, the experimental results demonstrate that the algorithm efficiently verifies the user-proposed flight trajectory and promptly identifies flight conflicts during the trajectory negotiation and verification processes. The algorithm then analyzes the flight trajectories of aircrafts by applying various constraints based on the specific traffic environment; the flight combinations which satisfy constraints can be identified. Then, based on the results identified by the algorithm, the air traffic management system can negotiate with users to adjust the flight trajectory, so as to reduce flight delay and ensure flight safety.