  We study properties of moving relativistic quantum unstable systems. We show
that in contrast to the properties of classical particles and quantum stable
objects the velocity of moving freely relativistic quantum unstable systems can
not be constant in time. We show that this new quantum effect results from the
fundamental principles of the quantum theory and physics: It is a consequence
of the principle of conservation of energy and of the fact that the mass of the
quantum unstable system is not defined. This effect can affect the form of the
decay law of moving relativistic quantum unstable systems.
