  The azimuthal correlations between local flow planes at different
(pseudo)rapidities ($\eta$) may reveal important details of the initial nuclear
matter density distributions in heavy-ion collisions. Extensive experimental
measurements of a factorization ratio ($r_2$) and its derivative ($F_2$) have
shown evidence of the longitudinal flow-plane decorrelation. However, nonflow
effects also affect this observable and prevent a quantitative understanding of
the phenomenon. In this paper, to distinguish decorrelation and nonflow
effects, we propose a new cumulant observable, $T_2$, which largely suppresses
nonflow. The technique sensitivity to different initial-state scenarios and
nonflow effects are tested with a simple Monte Carlo model, and in the end, the
method is applied to events simulated by a multiphase transport model (AMPT)
for Au+Au collisions at $\sqrt{s_{\rm NN}} =200$ GeV. We also emphasize that a
distinct decorrelation signal requires not only the right sign of an
observable, but also its proper dependence on the $\eta$-window of the
reference flow plane, to be consistent with the pertinent decorrelation
picture.
