<p>The article discusses the problem of a near-geostationary orbit determination. An innovative algorithm is developed, which uses only two pairs of angles of the right ascension and declination in order to obtain the orbital parameters. Only one short tracklet can be used for data extraction. The traditional approaches are usually based on Laplace and Gauss methods calling for three pairs of angles to solve the problem. The new approach is based on the use of linearised dimensionless equations of motion, which were previously used in the problem of calculating orbital manoeuvres. The results obtained are refined in a special iterative procedure. The proposed algorithm is also applicable if measurements are obtained on different revolutions, while this option is not possible for existing practices. The simplicity and the reliability of the suggested solution ensure effective maintenance of the catalogue in the vicinity of the geostationary Earth orbit. The examples of orbit determination are given and described in details.</p>