  The unextendible entangled basis with any arbitrarily given Schmidt number
$k$ (UEBk) in $\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}$ is proposed in [Phys.
Rev. A 90 (2014) 054303], $1<k\leq \min\{d_1,d_2\}$, which is a set of
orthonormal entangled states with Schmidt number $k$ in a $d_1\otimes d_2$
system consisting of fewer than $d_1d_2$ vectors which have no additional
entangled vectors with Schmidt number $k$ in the complementary space. In this
paper, we extend it to multipartite case and a general way of constructing
$(m+1)$-partite UEBk from $m$-partite UEBk is proposed ($m\geq 2$).
Consequently, we show that there are infinitely many UEBks in
$\mathbb{C}^{d_1}\otimes\mathbb{C}^{d_2}\otimes\cdots\otimes\mathbb{C}^{d_N}$
with any dimensions and any $N\geq3$.
