  Coupled Majorana zero modes with nonzero energies are generally detrimental
to the non-Abelian statistics due to the additional dynamic phase.
Nevertheless, we show that a well-connected lead can introduce a local
non-Hermitian dissipation term to shift the energies of the both coupled
Majorana modes to zero, and surprisingly turn the coupled Majorana mode far
from the lead into a dark Majorana mode with exponentially small dissipation.
This dark Majorana mode can conquer the drawback of the partially overlapped
Majorana zero modes and possess the properties of true Majorana zero mode such
as the perfect fractional Josephson effect and the non-Abelian statistics.
