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We introduce a new Möbius invariant, -hyperbolic metric for domains D in , which can be considered as a Möbius invariant analogue of the scale-invariant Cassinian metric recently introduced by the author. We establish basic properties of including its connections with , the Apollonian metric, Seittenranta’s metric and the hyperbolic metric. We also show that is monotonic with respect to domains, its density is the same as the density of Ferrand’s metric and that the -isometries of twice-punctured spaces are Möbius maps.