  We present the zero temperature phase diagram of the bond alternating Ising
chain in the presence of Dzyaloshinskii-Moriya interaction. An abrupt change in
ground state fidelity is a signature of quantum phase transition. We obtain the
renormalization of fidelity in terms of quantum renormalization group without
the need to know the ground state. We calculate the fidelity susceptibility and
its scaling behavior close to quantum critical point (QCP) to find the critical
exponent which governs the divergence of correlation length. The model consists
of a long range antiferromagnetic order with nonzero staggered magnetization
which is separated from a helical ordered phase at QCP. Our results state that
the critical exponent is independent of the bond alternation parameter (lambda)
while the maximum attainable helical order depends on lambda.
