  The origin of high velocity stars observed in the halo of our Galaxy is still
unclear. In this work we test the hypothesis, raised by results of recent high
precision $N$-body simulations, of strong acceleration of stars belonging to a
massive globular cluster orbitally decayed in the central region of the host
galaxy where it suffers of a close interaction with a super massive black hole,
which, for these test cases, we assumed $10^8$ M$_\odot$ in mass.
