  In this paper, we mainly consider the local indistinguishability of the set
of mutually orthogonal bipartite generalized Bell states (GBSs). We construct
small sets of GBSs with cardinality smaller than $d$ which are not
distinguished by one-way local operations and classical communication (1-LOCC)
in $d\otimes d$. The constructions, based on linear system and Vandermonde
matrix, is simple and effective. The results give a unified upper bound for the
minimum cardinality of 1-LOCC indistinguishable set of GBSs, and greatly
improve previous results in [Zhang \emph{et al.}, Phys. Rev. A 91, 012329
(2015); Wang \emph{et al.}, Quantum Inf. Process. 15, 1661 (2016)]. The case
that $d$ is odd of the results also shows that the set of 4 GBSs in $5\otimes
5$ in [Fan, Phys. Rev. A 75, 014305 (2007)] is indeed a 1-LOCC
indistinguishable set which can not be distinguished by Fan's method.
