The relaminarization phenomenon in the laminar–turbulent transition process of spherical Couette flow with the inner sphere rotating and the outer sphere fixed has been experimentally investigated for $0.06\,{ \leqslant}\,\beta\,{\leqslant}\,0.206$, where $\beta$ is the ratio of the clearance to the inner-sphere radius. The relaminarization occurs for $0.13\,{<}\,\beta\,{<}\,0.17$, and is observed as a reverse Hopf bifurcation from the limit cycle to the fixed point. The kinetic energy in the high-frequency region of the fluctuating azimuthal velocity component continues to increase with Reynolds number Re in the case without relaminarization, but in the case with relaminarization it first increases and then decreases with increasing Re and finally vanishes with the onset of the relaminarization. For $\beta\,{=}\,0.14$ with relaminarization, a small artificial disturbance introduced externally into the spherical Couette flow has no influence on the lowest critical Reynolds number of the first instability that can be defined universally and uniquely. On the other hand, the external disturbance decreases the onset Reynolds numbers of both the second instability (occurrence of spiral Taylor–Görtler (TG) vortices) and the relaminarization, although it has no influence on the fundamental frequencies of velocity fluctuation caused by spiral TG vortices and travelling waves on TG vortices.