  A more conventional realization of a symmetry which had been proposed towards
the solution of cosmological constant problem is considered. In this study the
multiplication of the coordinates by the imaginary number $i$ in the literature
is replaced by the multiplication of the metric tensor by minus one. This
realization of the symmetry as well forbids a bulk cosmological constant and
selects out $2(2n+1)$ dimensional spaces. On contrary to its previous
realization the symmetry, without any need for its extension, also forbids a
possible cosmological constant term which may arise from the extra dimensional
curvature scalar provided that the space is taken as the union of two $2(2n+1)$
dimensional spaces where the usual 4-dimensional space lies at the intersection
of these spaces. It is shown that this symmetry may be realized through
spacetime reflections that change the sign of the volume element. A possible
relation of this symmetry to the E-parity symmetry of Linde is also pointed
out.
