fermion doubling problem in deconstruction models

Hi,

lately, I have been trying to deconstruct orbifold models with one
extra dimension i.e. S1/Z_2 models but I am running into a serious
problem. Deconstruction is the process of replacing the continuous
fifth dimension with a finite number of points. The problem I am having
is that I encounter fermion doublings for bulk fermion fields as well
as N=1 chiral multiplets. This is driving me crazy. Do you know what I
should do?

I HAVE noticed that I can replace bulk fermion fields with two "chains"
across the deconstructed points. The real problem is that I can't
simply pick one chain and discard the other because some brane
interactions couple to one chain and others couple to the other and I
need both interactions.

.