  An entangled basis with fixed Schmidt number $k$ (EBk) is a set of
orthonormal basis states with the same Schmidt number $k$ in a product Hilbert
space $\mathbb{C}^d\otimes\mathbb{C}^{d'}$. It is a generalization of both the
product basis and the maximally entangled basis. We show here that, for any
$k\leq\min\{d,d'\}$, EBk exists in $\mathbb{C}^d\otimes\mathbb{C}^{d'}$ for any
$d$ and $d'$. Consequently, general methods of constructing SEBk (EBk with the
same Schmidt coefficients) and EBk (but not SEBk) are proposed. Moreover, we
extend the concept of EBk to multipartite case and find out that the
multipartite EBk can be constructed similarly.
