  We consider a single 3-brane situated between two bulk spacetimes that posses
the same cosmological constant, but whose metrics do not posses a
$Z_{2}$-symmetry. On each side of the brane, the bulk is a solution to
Gauss-Bonnet gravity. This asymmetry modifies junction conditions, and so new
terms arise in the Friedmann equation. If these terms become dominant, these
behave cosmological constant at early times for some case, and might remove the
initial singularity for other case. However, we show that these new terms can
not become dominant ones under usual conditions when our brane is outside an
event horizon. We also show that any brane-world scenarios of this type revert
to a $Z_{2}$-symmetric form at late times, and hence rule out certain proposed
scenarios.
