The Gehring--Martin--Tan inequality for two-generator subgroups of PSL(2; C) is one of the best known discreteness conditions. A Kleinian group G is called a Gehring--Martin--Tan group if the equality holds for the group G. We give a method for constructing Gehring--Martin--Tan groups with a generator of order four and present some examples. These groups arise as groups of finite-volume hyperbolic 3-orbifolds.