In this paper we propose a modified construction for the polynomial basis on polygons used in the Virtual
Element Method (VEM). This construction is alternative to the usual monomial basis used in the classical
construction of the VEM and is designed in order to improve numerical stability. For badly shaped elements the
construction of the projection matrices required for assembling the local coefficients of the linear system within
the VEM discretization of Partial Differential Equations can result very ill conditioned. The proposed approach
can be easily implemented within an existing VEM code in order to reduce the possible ill conditioning of the
elemental projection matrices. Numerical results applied to an hydro-geological flow simulation that often
produces very badly shaped elements show a clear improvement of the quality of the numerical solution,
confirming the viability of the approach. The method can be conveniently combined with a classical
implementation of the VEM and applied element-wise, thus requiring a rather moderate additional numerical
cost