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In this work, an implicit Lagrangian for the dual twin support vector regression is proposed. Our formulation leads to determining non-parallel –insensitive down- and up- bound functions for the unknown regressor by constructing two unconstrained quadratic programming problems of smaller size, instead of a single large one as in the standard support vector regression (SVR). The two related support vector machine type problems are solved using Newton method. Numerical experiments were performed on a number of interesting synthetic and real-world benchmark datasets and their results were compared with SVR and twin SVR. Similar or better generalization performance of the proposed method clearly illustrates its effectiveness and applicability.