  The scattering matrix $S$ obeys the unitary relation $S^\dagger S=1$ in a
Hermitian system and the symmetry property ${\cal PT}S{\cal PT}=S^{-1}$ in a
Parity-Time (${\cal PT}$) symmetric system. Here we report a different symmetry
relation of the $S$ matrix in a one-dimensional heterostructure, which is given
by the amplitude ratio of the incident waves in the scattering eigenstates. It
originates from the optical reciprocity and holds independent of the
Hermiticity or $\cal PT$ symmetry of the system. Using this symmetry relation,
we probe a quasi-transition that is reminiscent of the spontaneous symmetry
breaking of a $\cal PT$-symmetric $S$ matrix, now with unbalanced gain and loss
and even in the absence of gain. We show that the additional symmetry relation
provides a clear evidence of an exceptional point, even when all other
signatures of the $\cal PT$ symmetry breaking are completely erased. We also
discuss the existence of a final exceptional point in this correspondence,
which is attributed to asymmetric reflections from the two sides of the
heterostructure.
