  The instanton-noninstanton (I-NI) transition in the tunneling process, which
has been numerically observed in classically nonintegrable quantum maps, can be
described by a perturbation theory based on an integrable Hamiltonian
renormalized so as to incorporate the integrable part of the map. The
renormalized perturbation theory is successfully applied to the two quantum
maps, the H\'enon and standard maps. In spite of different nature of tunneling
in the two systems, the I-NI transition exhibits very common characteristics.
In particular, the manifestation of I-NI transition is obviously explained by a
remarkable quenching of the renormalized transition matrix element. The
enhancement of tunneling probability after the transition can be understood as
a sudden change of the tunneling mechanism from the instanton to quite a
different mechanism supported by classical flows just outside of the
stable-unstable manifolds of the saddle on the top of the potential barrier.
