The Chandrasekhar H-function plays an important role in a wide class of problems of analytical radiative transfer theory. The H-function is the solution of well-known integral equations, both non-linear and linear. The physics of a particular problem under consideration determines the form of the so-called characteristic and dispersion functions, Ψ(μ) and T(μ), respectively. They appear in H-equations and determine their solutions. We show that Ψ(μ) and T(μ) can be restructured in such a way that the solutions of H-equations transforms from H(μ) to Hⁿ(μ),n=2,3,4,… provided Ψ(μ) and T(μ) are replaced with Ψ_n(μ) and T_n(μ). The structure of the non-linear and linear H-equations does not change under this transformation. The basis of this restructuring is a recursion relation that gives Ψ_n(μ) and T_n(μ) in terms of Ψ(μ) and T(μ).