  Recently the splitting of elliptic flow $v_2$ at finite rapidities has been
proposed as a result of the global vorticity in non-central relativistic heavy
ion collisions. In this study, we find that this left-right (i.e., on opposite
sides of the impact parameter axis) splitting of the elliptic flow at finite
rapidities is a result of the non-zero directed flow $v_1$, with the splitting
magnitude $\approx 8v_1(1-3v_2)/(3\pi)$. We also use a multi-phase transport
model, which automatically includes the vorticity field and flow fluctuations,
to confirm the $v_2$ splitting. In addition, we find that the analytical
expectations for the $v_2$ splitting work for the raw $v_2$ and $v_1$ (i.e.,
before event plane resolutions are applied) measured relative to either the
first- or second-order event plane. Since the $v_2$ splitting is mostly driven
by $v_1$, it vanishes at zero transverse momentum ($p_{\rm
  T}$), and its magnitude and sign may have non-trivial dependencies on $p_{\rm
T}$, centrality, collision energy, and hadron species.
