  We show that gyrotropic structures with balanced gain and loss that respect
anti-linear symmetries exhibit a giant non-reciprocity at the so-called exact
phase where the eigenfrequencies of the isolated non-Hermitian set-up are real.
The effect occurs in a parameter domain near an exceptional point (EP)
degeneracy, where mode-orthogonality collapses. The theoretical predictions are
confirmed numerically in the microwave domain, where a non-reciprocal transport
above 90dB is demonstrated, and are further verified using lump-circuitry
modeling. The analysis allows us to speculate the universal nature of the
phenomenon for any wave system where EP and gyrotropy can co-exist.
