  $\textbf{Background:}$ The chiral magnetic effect (CME) is extensively
studied in heavy-ion collisions at RHIC and LHC. In the commonly used reaction
plane (RP) dependent, charge dependent azimuthal correlator ($\Delta\gamma$),
both the close and back-to-back pairs are included. Many backgrounds contribute
to the close pairs (e.g. resonance decays, jet correlations), whereas the
back-to-back pairs are relatively free of those backgrounds.
  $\textbf{Purpose:}$ In order to reduce those backgrounds, we propose a new
observable which only focuses on the back-to-back pairs, namely, the relative
back-to-back opposite-sign (OS) over same-sign (SS) pair excess
($r_{\text{BB}}$) as a function of the pair azimuthal orientation with respect
to the RP ($\varphi_{\text{BB}}$).
  $\textbf{Methods:}$ We use analytical calculations and toy model simulations
to demonstrate the sensitivity of $r_{\text{BB}}(\varphi_{\text{BB}})$ to the
CME and its insensitivity to backgrounds.
  $\textbf{Results:}$ With finite CME, the $\varphi_{\text{BB}}$ distribution
of $r_{\text{BB}}$ shows a clear characteristic modulation. Its sensitivity to
background is significantly reduced compared to the previous $\Delta\gamma$
observable. The simulation results are consistent with our analytical
calculations.
  $\textbf{Conclusions:}$ Our studies demonstrate that the
$r_{\text{BB}}(\varphi_{\text{BB}})$ observable is sensitive to the CME signal
and rather insensitive to the resonance backgrounds.
