  The non-Hermitian skin effect (NHSE), an anomalous localization behavior of
the bulk states, is an inherently non-Hermitian phenomenon, which can not find
a counterpart in Hermitian systems. However, the fragility of NHSE has been
revealed recently, such as the boundary sensitivity, and it stimulates a lot of
studies on discussing the fate of that. Here we present a theorem which shows
that the combined spatial reflection symmetry can be considered as a criterion
in one-dimensional non-Hermitian systems to determine whether the NHSE can
exist or not. Distinct from previous studies, our proposed criterion only
relies on analyzing the symmetry of the system, freeing out other requirements,
such as the information of the energy spectrum. Furthermore, by taking the
non-Hermitian Kitaev chain as an example, we verify our theorem through both a
mathematical proof via the non-Bloch band theory and the exact diagonalization
numerical studies. Our results reveal a profound connection between the
symmetry and the fate of NHSE.
