In this letter, we decode the newly observed charmoniumlike states, Y(4320) and Y(4390), by introducing interference effect between psi (4160) and psi (4415), which plays a role of resonance killer for Y(4320) and Y(4390). It means that two newly reported charmoniumlike states are not genuine resonances, according to which we can naturally explain why two well-established charmonia psi (4160) and psi (4415) are missing in the cross sections of e^+e^- rightarrow pi ^+ pi ^- J/psi and pi ^+ pi ^- h_c simultaneously. To well describe the detailed data of these cross sections around sqrt{s}=4.2 GeV, our study further illustrates that a charmoniumlike structure Y(4220) must be introduced. As a charmonium, Y(4220) should dominantly decay into its open-charm channel e^+e^- rightarrow D^0 pi ^+ D^{*-}, which provides an extra support to psi (4S) assignment to Y(4220). In fact, this interference effect introduced to explain Y(4320) and Y(4390) gives a typical example of non-resonant explanations to the observed XYZ states, which should be paid more attention especially before identifying the observed XYZ states as genuine resonances.
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