The effective simulation of the Δ²-distribution is discussed. It has been considered so far that the only simulation method applicable to the Δ²-distribution is the rejection one. An approach, making use of the inversion, composition, and rejection methods at the same time, which significantly decreases simulation complexity, is proposed. The advantage is obtained due to the structure of the conditional densities, which was first discovered by the authors. The paper presents the simulation algorithm, proofs of the theorems on the form of the conditional densities and a complexity comparison between the suggested method and the pure rejection.