  We study the modifications of the generalized permutation branes defined in
hep-th/0509153, which are required to give rise to the non-factorizable branes
on a product of cosets $G_{k_1}/H\times G_{k_2}/H$. We find that for $k_1\neq
k_2$ there exists big variety of branes, which reduce to the usual permutation
branes, when $k_1=k_2$ and the permutation symmetry is restored.
