  The unextendible product basis (UPB) is generalized to the unextendible
entangled basis with any arbitrarily given Schmidt number $k$ (UEBk) for any
bipartite system $\mathbb{C}^d\otimes\mathbb{C}^{d'}$ ($2\leq k<d\leq d'$),
which can also be regarded as a generalization of the unextendible maximally
entangled basis (UMEB). A general way of constructing such a basis with
arbitrary $d$ and $d'$ is proposed. Consequently, it is shown that there are at
least $k-r$ (here $r=d$ mod $k$, or $r=d'$ mod $k$) sets of UEBk when $d$ or
$d'$ is not the multiple of $k$, while there are at least $2(k-1)$ sets of UEBk
when both $d$ and $d'$ are the multiples of $k$.
