A simple normal-moveout (NMO) correction can move common-depth-point (CDP) reflection times up or down a few milliseconds when the stacking velocity is varied a small fraction. Different stacking velocities on two orthogonal shear components are often required, such as in the cases of azimuthal anisotropic media or transversely isotropic media. The difference between these two cases is that CDP reflection times are different on S1 and S2 in the case of azimuthal anisotropy, while CDP reflection times are equal for transverse isotropic media. The similarity is that both cases require different stacking velocities on the S1 and S2 components. Careful studies have proven the existence of detectable azimuthal anisotropy in CDP shear-wave data. The potential problem addressed in this note is the new seismic pitfall created if the basic effects of NMO are forgotten. About 14 ms of false shear anisotropy is demonstrated by a simple synthetic seismogram.