$d$ locally indistinguishable maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$

We give a explicit construction of $d$ locally indistinguishable orthogonal maximally entangled states in ${\mathbb{C}}^d\otimes {\mathbb{C}}^d$ for any $d\ge 4$. This gives an answer to the conjecture proposed by S. Bandyopadhyay in 2009. Thus it reflects the nonlocality of the fundamental feature of quantum mechanics.