$textbf{Background:}$ 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 ($Deltagamma$), 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 $Deltagamma$ 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.
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