The distribution of the angle between the arrival directions of the fronts of consecutive Extensive Air Showers(EAS) with a wide range of a total number of charged particles is studied using the experimental data taken by the EAS 4-detector array TEL in Telavi. The station is a part of the GELATICA net in Georgia (GEorgian Large-area Angle and TIme Coincidence Array), which is devoted to the study of possible correlations in the arrival times and directions of separate EAS events over large distances. It is shown that the aforementioned directions really are in the essentially independent and can be used for investigation of simultaneous correlations of the EAS arrival times and directions.