  The balanced hypercube, $BH_n$, is a variant of hypercube $Q_n$. R.X. Hao et
al. $(2014)$ \cite{R.X.Hao} showed that there exists a fault-free Hamiltonian
path between any two adjacent vertices in $BH_n$ with $(2n-2)$ faulty edges.
D.Q. Cheng et al. $(2015)$ \cite{Dongqincheng2} proved that $BH_n$ is
$6$-edge-bipancyclic after $(2n-3)$ faulty edges occur for all $n\ge2$. In this
paper, we improve these two results by demonstrating that $BH_n$ is
$6$-edge-bipancyclic even when there exist $(2n-2)$ faulty edges for all
$n\ge2$. Our result is optimal with respect to the maximum number of tolerated
edge faults.
