A distinct ESR (electron spin resonance) signal was found to overlap the E1′ centre signal in natural quartz irradiated by γ-rays. Its g-value is identical to the signal of the E1′ centre and its intensity begins to saturate below a microwave power of 0.4 mW, as does that of the E1′ centre. The shape of this signal shows one peak, whereas the “real” E1′ centre signal is almost axial, having two peaks. The overlapping signal was found to be very unstable and its half life was estimated to be 28 years at 15°C (mean life of 40 years). We named it the “counterfeit E1′ signal”. We show the necessity of examining the signal shape and the thermal stability of the supposed E1′ signal observed in natural quartz irradiated by γ-rays.