  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 $\epsilon_M\to
0$. 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 $\epsilon_M\to 0$. 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 in practical measurement, are accessible directly. For
different bias voltage setup, we find intriguing 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 definitely confirm the existence of the nonlocal MZMs.
