This paper presents a new functional computation model for developing a class of two-variable Lambda-Boolean functions, and describes the properties of the duality principle on this model. With respect to this aim, some definitions and theorems which construct the model of the two-variable Lambda-Boolean functions are given. The simulation of the model is implemented in the programming language Prolog, and the whole code is given as an extended and revised version of the implementation in [S. Mirasyedioglu, T. Guyer, A symbolic and algebraic computation based Lambda-Boolean reduction machine via PROLOG, Appl. Math. Comput. 176 (1) (2006) 65-75]. (c) 2006 Elsevier Inc. All rights reserved.