Existing studies via shot noise calculation conclude that the cross correlation between the currents in the two leads connected by a pair of Majorana zero modes (MZMs) vanishes when their coupling energy εM → 0.Motivated by the intrinsic nature of nonlocality of the MZMs,we revisit this important problem and propose an experimental scheme to demonstrate the nonvanishing cross correlation even at the limit εM → 0.The proposed scheme employs the Andreev-process-associated branch circuit currents,which are theoretically obtained by applying a decomposition analysis for the total currents while are accessible directly in practical measurement.For different bias voltage setup,we find intrigu-ing results of both negative and positive correlations and carry out simple physical understanding using a quantum jump technique.Importantly,combining together with the evidence of the zero-bias-peak of conductance,the nonlocal cross correlation predicted in this work can help to confirm the existence of the nonlocal MZMs.