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The given publication can be of interest to those, who have ever tried to comprehend the paradoxes of the spesial theory of relativity. The transformations of coordinates and time for high-energy particles and extended objects in inertial reference systems are obtained by the author taking into account the initial conditions of motion. It is shown that the events simultaneous in different points of the same inertial reference system will also be simultaneous in some other inertial reference systems. The linear sizes of the extended objects, of the solid bodies and the orbital formations of space in different inertial reference systems remain unchanged.