The Cassinian metric of a proper domain \(D\) in \(\mathbb{R}^n\) is defined by \[ c_D(x,y)=\sup_{p\in \partial D}\frac{|x-y|}{|x-p||p-y|}. \] In the paper under review the scale-invariant Cassinian metric \(\tilde{\tau}_D\) is introduced as \[ \tilde{\tau}_D(x,y)=\log\left(1+\sup_{p\in \partial D}\frac{|x-y|}{\sqrt{|x-p||p-y|}}\right). \] The author gives basic properties of \(\tilde{\tau}_D\) and inequalities by comparing it with other hyperbolic-type metrics such as \(j\)-metric, \(\tilde{j}\)-metric, the half-Apollonian metric, and the hyperbolic metric. One of the results for \(D=\mathbb{R}^n\setminus \{p\}\) is that \(\tilde{\tau}_D\) is invariant under Möbius transformations of \(D\). For the density of \(\tilde{\tau}_D\) for a proper domain \(D\) the author shows that it is the same as the density of quasihyperbolic metric. Furthermore, when \(D\) is the unit ball \(\mathbb{B}^n\), the author shows distortion properties of \(\tilde{\tau}_D\) under Möbius transformations of \(\mathbb{B}^n\).