A multi-stage safe formation transformation method for Unmanned Aerial Vehicles (UAVs) formation is proposed to address the problem that rotary-wing UAVs formation passes through narrow corridors at high speed while maintaining a similar formation configuration as much as possible. Firstly, the center of the UAVs formation is regarded as a virtual leader. According to the kinematic constraints of UAVs, a mixed-integer linear programming method is used to plan a smooth and high-speed virtual leader trajectory with the maximum distance from obstacles and the safe flight space of the entire formation. Then, based on the safe flight space of the formation and the virtual leader trajectory, a formation configuration without external and internal collisions and with minimum changes compared with the initial configuration is obtained. Subsequently, based on the generated formation configuration and the virtual leader trajectory, the desired trajectories of each UAV are calculated in a distributed manner. A distributed algorithm combining nonlinear optimization and cooperative time redistribution is proposed to optimize the trajectories of each UAV, so that high-speed flight and formation maintenance can be achieved while satisfying the kinematic constraints. Simulation results show that the proposed method enables the UAVs formation to pass through narrow corridors safely and at high speed while satisfying the kinematic constraints, and maintains a formation configuration close to the initial configuration as much as possible.