Summary: Let \(\mathbb{F}_{q^2}\) be a finite field of order \(q^2\) and \(2\nu +\delta\geq 2\) be an integer with \(\delta =0\) or \(1\), where \(q\) is a power of a prime. We introduce the concept of the unitary inner product graph \(Ui(2\nu +\delta, q^2)\) over \(\mathbb{F}_{q^2}\) and determine its automorphism group. We obtain two necessary and sufficient conditions for two vertices of \(Ui(2\nu +\delta, q^2)\) and two edges of \(Ui(2\nu +\delta, q^2)\), respectively, are in the same orbit under the action of the automorphism group of \(Ui(2\nu +\delta, q^2)\).