Nuclear quadrupole resonance results on the inorganic spin-Peierls compound CuGeO₃ were re-examined using a single crystal and enhanced resolution. A clear splitting of ^63,65 Cu NQR lines of about 250 kHz at 4.2 K was observed. Such a splitting has not been previously seen in Cu NQR spectra measured on polycrystalline samples of CuGeO₃ (Itoh M et al 1995 Phys. Rev. B 52 3410, Kikuchi et al 1994 J. Phys. Soc. Japan 63 872). The mean frequency of the Cu doublet is in agreement with the Cu NQR frequency observed on powder samples. The splitting does not disappear with increasing temperature above T_sP exhibiting only a slight kink at around 16 K. This points to a non-magnetic origin of the splitting which can be attributed to existence of at least two non-equivalent Cu crystal sites in CuGeO₃ structure, as predicted by precise x-ray study and EPR measurements (Hidaka M et al 1997 J. Phys.: Condens. Matter 9 809, Yamada I et al 1996 J. Phys.: Condens. Matter 8 2625).