On the basis of the similarity of seismic waveforms and shapes of the reflectors, the coherence and curvature attributes can be derived, respectively, to characterize faults. Coherence is effective for characterizing relatively large faults. When the distortion of seismic waveforms at a fault is not obvious, the curvature attribute may play a complementary role in detecting the fault. According to geometric features of the faulted strata, the rate of change of curvature has recently been developed to improve fault characterization. Through an application to the real seismic data from the western Tazhong area of the Tarim Basin, China, it was demonstrated that curvature change rate has advantages in detecting subtle faults having quite small throws and heaves. However, when the dip angle of a faulted stratum is smaller than 45°, the curvature change rate derived from its fitted surface has multiple extreme values associated with one fault plane, which cause a low signal-to-noise ratio (S/N) of a computation result for the multiple extrema interfering with each other. To overcome this shortcoming, we first implement a rotation and stretching transformations of the seismic samples and then fit a cylindrical surface to the transformed samples. The curvature change rate of the directrix of the cylindrical surface is used to characterize faults. Through its application to 3D seismic data from the western Tazhong area in the Tarim Basin, the result indicates that in comparison with the previous curvature change rate, the new method significantly improves the S/N of the calculated result.