In the last few years, Scientific Machine Learning is rapidly gaining more and more popularity, and numerous methods that combine Machine Learning techniques with classical numerical methods are emerging. The advantage of such hybrid methods is that they can take advantage of the rigorous and accurate nature of classical numerical methods, while relying on the flexibility and non-linearity of neural networks (or alternative techniques) to mitigate some of their disadvantages. In particular, we focus on the Neural Approximated Virtual Element Method (NAVEM) [1,2], which is a polygonal method that approximates via a neural network the basis functions of the Virtual Element Method (VEM). Indeed, VEM is a polygonal method whose basis functions are not available in closed form, and that therefore relies on suitable stabilization and projection operators. In the NAVEM framework, instead, the VEM basis functions are accurately approximated by a neural network, which expression (available in closed form) is directly used to compute all the involved differential operators through standard quadrature. In the formulation proposed in [1,2], the neural network looks for a candidate function in a prescribed function space that accurately approximates the VEM basis function. However, this operation leads to higher computational costs and functions that are not continuous on the interface between different elements. To address these two issues, we propose an alternative formulation that ensures exact global continuity and does not require the generation of an approximation function space. In such formulation, inspired by [3], the neural network's output is modified in order to exactly coincide with the VEM basis function it is approximating, ensuring the global continuity of the corresponding basis functions. Numerical experiments are presented to show the effectiveness of the method and compare it with the NAVEM standard formulation and the VEM. [1] S. Berrone, D. Oberto, M. Pintore, and G. Teora The lowest-order neural approximated virtual element method, ENUMATH 129–138 (2025). [2] S. Berrone, M. Pintore, and G. Teora The lowest-order neural approximated virtual element method on polygonal elements, Computers & Structures 314, 107753 (2025). [3] S. Berrone, C. Canuto, M. Pintore, and N. Sukumar Enforcing Dirichlet boundary conditions in physics-informed neural networks and variational physics-informed neural networks, Heliyon, 9(8) (2023).