This paper analyzes the possibilities of a new method to using TLE data for detecting satellite maneuvers. The method has a number of advantages over other methods that are designed to detect maneuvers. It allows not only to detect maneuvers, but also to get a more complete picture of the maneuver. In particular, the method makes it possible to estimate the moments of the beginning and end of the maneuver, calculate the changes in the orbital elements, evaluate the tangential and binormal components of the impulse, and finally, calculate the impulse of the satellite obtained as a result of the maneuver. To demonstrate in detail the capabilities of the algorithm, the proposed method was applied to one of LEO satellites - TIANHUI-1 satellite. After the efficiency of the method was proved, this method was applied to the China Space Station - TIANHE-1 (CSS), Starlink-1095 and Starlink-2305 satellites. The maneuvers of the CSS and Starlink-1095 satellite during their close encounter on 1 July, 2021, and the CSS and Starlink-2305 satellite during their close encounter on 21 October, 2021 are analyzed in detail. The minimum distances between the CSS and Starlink satellites at the moments of their maximum approaches are estimated. An estimate of the computation time of this algorithm is given, and the possibility of its use for monitoring maneuvers or other anomalous orbital changes of a large number of satellites in near real-time is shown. It is assumed that on the basis of this method, a service for monitoring satellite maneuvers can be created.