The ratio of KSKS (KLKL) and KSKL production rates is calculated by considering K 0 − K 0 oscillation in J/ψ → K 0 K 0 decay. The theoretical uncertainty due to strong interaction in J/ψ decay is completely canceled in the ratio, therefore, the absolute branching fractions of the CP violating processes of J/ψ → KSKS and KLKL can be cleanly and model-independently determined in case that J/ψ → KSKL decay is precisely measured. In the future τ -Charm factory, the expected CP violating process of J/ψ → KSKS should be reached. It is important to measure J/ψ to KSKS and KSKL decays simultaneously, so that many systematic errors will be canceled. More precise measurements are suggested to examine the predicted isospin relation in J/ψ → KK decays. All results can be extended to decays of other vector quarkonia, φ, ψ(2S) and Υ (1S) and so on.PACS numbers: 13.25. Gv, 11.30.Er In the Standard Model (SM), CP violation arises from an irreducible weak phase in the Cabibbo-KobayashiMaskawa (CKM) quark-mixing matrix [1]. CP violation has been established in both K and B systems. Currently, all experimental measurements are consistent with the CKM picture of CP violation, and the CKM is, very likely, the dominant source of CP violation in low energy flavor-changing processes [2]. However, the surprising point is that the CKM mechanism for CP violation fails to account for the baryogenesis [3]. It is crucial to probe CP violation in various reactions, to see the correlations between different processes and probe the source of CP violation.In this Letter, we consider the possible CP asymmet-Within the SM, the possible CP violating decay processes of J/ψ → K S K S and K L K L are due to K 0 − K 0 oscillation, here we assume that possible strong multiquark effects that involve seaquarks play no role in. The J/ψ decays will provide another opportunity to understand the source of CP violation. The amplitude for J/ψ decaying to0 |H|J/ψ , and the K 0 K 0 pair system is in a state with charge parity C = −1, which can be defined asAlthough there is weak current contribution in J/ψ → K 0 K 0 decay, which may not conserve charge parity, the K 0 K 0 pair can not be in a state with C = +1. The reason is that the relative orbital angular momentum of K 0 K 0 pair must be l = 1 because of angular momentum conservation. A boson-pair with l = 1 must be in an antisymmetric state, the anti-symmetric state of particleanti-particle pair must be in a state with C = −1. This conclusion can also be illustrated by a direct calculation.For explicitness, let us denote the particle state |K 0 with momentum p 1 as |K 0 (p 1 ) , and |K 0 with momentum p 2 as |K 0 (p 2 ) . The general structure of the effectivewhere q i (i = d, s) and c denote the quarks d, s and c, C W is the Wilson coefficient, and a, b, a ′ , b ′ are the relevant coefficients for the vector and axial-vector currents. Then the amplitude for J/ψ decaying into a state