  Critical transition points between symmetry-broken phases are characterized
as fixed points in the renormalization group (RG) theory. We show that,
following the standard Wilsonian procedure that traces out the large momentum
modes, this well known fact can break down in non-Hermitian systems. Based on
non-Hermitian Su-Schrieffer-Hegger (SSH)-type models, we propose a real-space
decimation scheme to study the criticality between the topological and trivial
phase. We provide concrete examples and an analytic proof to show that the
real-space scheme perfectly overcomes the insufficiency of the standard method,
especially in the sense that it always preserves the system at criticality as
fixed points under RG. The proposed method can also greatly simplify the search
of critical points for complicated non-Hermitian models by ruling out the
irrelevant operators. These results pave the way towards more advanced RG-based
techniques for the interacting non-Hermitian quantum systems.
