The unextendible product basis is generalized to the unextendible entangled basis with any arbitrarily given Schmidt number
k (UEBk) for any bipartite system ${\mathbb{C}}^{d}\ensuremath{\bigotimes}{\mathbb{C}}^{{d}^{\ensuremath{'}}}$ $(2\ensuremath{\le}k<d\ensuremath{\le}{d}^{\ensuremath{'}})$, which can also be regarded as a generalization of the unextendible maximally entangled basis. A general way of constructing such a basis with arbitrary
d and ${d}^{\ensuremath{'}}$ is proposed. Consequently, it is shown that there are at least $k\ensuremath{-}r$ (here
r=dmodk or $r={d}^{\ensuremath{'}}\phantom{\rule{0.16em}{0ex}}\text{mod}\phantom{\rule{0.28em}{0ex}}k)$ sets of UEBks when
d or ${d}^{\ensuremath{'}}$ is not a multiple of
k, while there are at least $2(k\ensuremath{-}1)$ sets of UEBks when both
d and ${d}^{\ensuremath{'}}$ are multiples of
k.