Let G\sbρ denote the Kleinian group with presentation$$\langle T\sb1, T\sb{i}, E\sb{\rho}, E\sb{i\rho}\mid\lbrack T\sb1, T\sb{i}\rbrack=1, \lbrack E\sb{\rho}, E\sb{i\rho}\rbrack=1\rangle.$$Let Ω(G\sbρ) be its region of discontinuity, Λ(G\sbρ) be its limit set and C\sbρ be the convex hull of Λ(G\sbρ). Let S be a subset of C consisting of all ρ for which H\sp3∪Ω(G\sbρ)/G\sbρ is a 3-manifold with two cusps Ω(G\sbρ)/G\sbρ is a genus two surface. S is a two-dimensional slice of the six dimensional deformation space of G\sbρ. Using Bers' theorem, we show that S is topologically an open annulus. All the groups in S are normalized by $R\sb{\pi/2}, $ the rotation about the origin through an angle of π/2. Consequently, R\sbπ/2 preserves the bending lamination. The quotient of the genus two surface Ω(G\sbρ)/G\sbρ by the action of $R\sb{\pi/2}, $ is an orbifold O whose underlying topological space is the 2-sphere, and which contains two order 2 cone points and two order 4 cone points. Any lamination that is invariant under R\sbπ/2 projects to a lamination on O. We show that the set of geodesic laminations that are invariant under R\sbπ/2 can be identified with ${\bf R}\cup{\infty}, $ and that all except the one corresponding to ∞ occur as bending laminations. Coordinates have been introduced on S that reflect the geometry of the pleated surface ∂C\sbρ/G\sbρ. The first coordinate represents the bending lamination and the second the normalized length of the bending lamination. The set of groups corresponding to a fixed $\lambda\in{\bf R}, $ coincides with a branch of the real locus of an analytic function. For $\lambda\in{\bf Q}, $ the lamination consists of closed geodesics, and the analytic function corresponds to the traces of the group elements that represent these closed curves. All these branches are disjoint and non-singular and it can be shown that the rational branches are dense in S by interpolating them with rays along which the pleating locus is an irrational lamination.