In order to investigate a possible origin for stars with high peculiar velocities in the thick disc of our Galaxy, the dynamical evolution of 16 000 three-dimensional triple systems which consist of a binary with equal or comparable masses of components M 1 and M 2 and a low-mass third body M 3 is considered. We examine an extensive range of initial conditions with positions of the body M 3 randomly distributed around and inside the binary orbit. M 3 was given the initial radial velocity V 0 with respect to the center of inertia of the binary. The following dynamical system of units is used in this work: the unit of distance is the semi-major axis of the binary orbit, the unit of time is the period of the binary; the universal constant of gravity is unity. In these units the total mass of the close binary is 4π2.