  Evolution of quantum fidelity for two-level systems is studied in the context
of periodic echo. From a general treatment for time independent case, we obtain
a simple condition on the governing Hamiltonians under which the systems
display periodic quantum echo. For a specific time dependent problem the
quantum fidelity is shown to exhibit Rabi oscillation. This may be considered
as a simple mechanism to generate periodic echo, except for a specific initial
superpositional state in which case the fidelity remains invariant.
