Jørgensen’s inequality gives a necessary condition for a nonelementary two generator subgroup of $SL(2,\mathbb{C})$ to be discrete. By embedding $SL(2,\mathbb{C})$ into $Û(1,1;\mathbb{H})$, we obtain a new type of Jørgensen’s inequality, which is in terms of the coefficients of involved isometries. We provide an example to show that this result gives an improvement over the classical Jørgensen’s inequality.
