The Chiral Magnetic Effect (CME) refers to charge separation along a strong magnetic field, due to topological charge fluctuations in QCD. Charge correlation (Δγ) signals consistent with CME have been first observed almost a decade ago. It has also been known since then that the Δγ is contaminated by a major background from resonance decays coupled with elliptic flow. In this contribution, we propose differential Δγ measurements as function of the pair invariant mass (minv). The Δγ in the high minv region is essentially free of resonance backgrounds. In the low minv region, the Δγ backgrounds show resonance peaks. The CME signal, presumably smooth in minv, may thus be extracted from a two-component model fit. We demonstrate the feasibility and effectiveness of this novel method by using the AMPT and toy-model Monte-Carlo simulations. We also discuss an application of the method in data analysis.