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Based on a sample of (10087 ± 44) × 10 6 J / ψ events collected at the center-of-mass energy GeV with the BESIII detector, we search for the charmonium rare weak decay . No significant signal is observed, and the upper limit on its decay branching fraction at the 90% confidence level is set as 1.4 × 10 − 7 , improving the sensitivity of the previous best limit by an order of magnitude.