A formulation for spinless particles, that holds true the formal equivalency of spatial and time particle’s coordinates achieved through the introduction of an auxiliary parameter of evolution, has been put forward in terms of relativistic quantum mechanics. The proposed modification of theory gave a space-time picture of elementary processes involved in a finite region of the Minkowsky space in the form of scattering amplitudes. In order to define the evolution parameter, an additional condition was introduced. That was the presence of an extreme of the scattering amplitude phase. The probabilistic interpretation of the scattering amplitude includes a contraction of integration measure in the Minkowsky space on a 3D-surface given by experimental conditions. The nonrelativistic limit of the modified theory was shown to coincide with the Schröedinger theory, including the dynamical model of the stationary scattering problem in terms of wave packets movement.